MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C9B84F.9DA3E1A0" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections

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The graphs of 2nd (quadratic) equations are called <= /span>parabolas. = Parabolas describe the paths of thrown objects (or the upside-= down path= s).
Graphs of Quadratic Equations
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The graphs of 2nd (quadratic) equations are called <= /span>parabolas. = Parabolas describe the paths of thrown objects (or the upside-= down path= s).
Graphs of Quadratic Equations
Properties of Parabola= s:
•<= /span>  Parabolas are symmetric with resp= ect to a center line
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file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0134_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAgB2AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAB AHMAgAAAAP8AAAISjA15Gwl8HERqSlvh1Zlt3y0FADs= ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0135.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
The graphs of 2nd (quadratic) equations are called <= /span>parabolas. = Parabolas describe the paths of thrown objects (or the upside-= down path= s).
Graphs of Quadratic Equations
Properties of Parabola= s:
•<= /span>  Parabolas are symmetric with resp= ect to a center line
•<= /span>  The highest or lowest point of the parabola sits on the   
   center line. 
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The graphs of 2nd (quadratic) equations are called <= /span>parabolas. = Parabolas describe the paths of thrown objects (or the upside-= down path= s).
Graphs of Quadratic Equations
Properties of Parabola= s:
•<= /span>  Parabolas are symmetric with resp= ect to a center line
•<= /span>  The highest or lowest point of the parabola sits on the   
   center line.  This point is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >vertex.<= /div>
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file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0136_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAkAgQAAAAAAAP9QUAECAwITBIJoJ93BnENyhvoupjvOlShAAQA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0136_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBgAFAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAD AAQAgAAAAP9mAAIERHyhWwA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0137.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
The graphs of 2nd (quadratic) equations are called <= /span>parabolas. = Parabolas describe the paths of thrown objects (or the upside-= down path= s).
Graphs of Quadratic Equations
Properties of Parabola= s:
•<= /span>  Parabolas are symmetric with resp= ect to a center line
•<= /span>  The highest or lowest point of the parabola sits on the   
   center line.  This point is called the <= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >vertex.<= /div>
Vertex Formula: The vertex of y =3D ax2 + bx + c is at x =3D     .
-b
2a
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file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0137_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAkAgQAAAAAAAP9QUAECAwITBIJoJ93BnENyhvoupjvOlShAAQA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0137_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0152.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
Graphs of Quadratic Equations
When graphing parabolas, we must also give the x-intercepts = = and the y-intercept.
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0153.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0154.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
The x-intercept is obt= ained by setting y =3D 0 and solve the equation 0 =3D ax2 + bx + c
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0155.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
The x-intercept is obt= ained by setting y =3D 0 and solve the equation 0 =3D ax2 + bx + c which may or may not have real number solutions.
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0156.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
The x-intercept is obt= ained by setting y =3D 0 and solve the equation 0 =3D ax2 + bx + c which may or may not have real number solutions. Hence there might not be any x-intercept.
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0157.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
The cente= r line is determined by the vertex.
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
The x-intercept is obt= ained by setting y =3D 0 and solve the equation 0 =3D ax2 + bx + c which may or may not have real number solutions. Hence there might not be any x-intercept.
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The center line is determined by the vertex. Suppose we know anot= her point on the parabola,
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
The x-intercept is obt= ained by setting y =3D 0 and solve the equation 0 =3D ax2 + bx + c which may or may not have real number solutions. Hence there might not be any x-intercept.
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The center line is determined by the vertex. Suppose we know anot= her point on the parabola, the reflection of the point across th= e center is also on the parabola. 
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
The x-intercept is obt= ained by setting y =3D 0 and solve the equation 0 =3D ax2 + bx + c which may or may not have real number solutions. Hence there might not be any x-intercept.
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image/gif R0lGODlhAwCEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAD AIEAgAAAAP8AAAIgjI+pCu0P45r0xAurZri7DRoeFoKjV25nl2pr1lLvtRUAOx== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0159_image056.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBACEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAC AIEAgAAAAP8AAAIcjI95wO2uYnoUyBtqxVJDrngPGIoNOZkoYp5RAQA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0160.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
The center line is determined by the vertex. Suppose we know anot= her point on the parabola, the reflection of the point across th= e center is also on the parabola. There is exactly one parab= ola that goes through these three points.
Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is (o,= c) obtained by setting x =3D 0.
The x-intercept is obt= ained by setting y =3D 0 and solve the equation 0 =3D ax2 + bx + c which may or may not have real number solutions. Hence there might not be any x-intercept.
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Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
Graphs of Quadratic Equations
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0162.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
-b=
2a=
Graphs of Quadratic Equations
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0162_image065.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0163.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
-b=
2a=
Graphs of Quadratic Equations
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0163_image066.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0164.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola.
-b=
2a=
Graphs of Quadratic Equations
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0164_image067.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0165.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
-b=
2a=
Graphs of Quadratic Equations
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0165_image068.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0166.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0166_image069.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0167.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
Example C. Graph y =3D –x + 2x + 15
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0167_image070.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0168.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
Example C. Graph y =3D –x + 2x + 15
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0168_image071.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0169.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Example C. Graph y =3D –x + 2x + 15
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0169_image072.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0170.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Example C. Graph y =3D –x + 2x + 15
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0170_image073.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0171.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
Example C. Graph y =3D –x + 2x + 15
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0171_image074.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0172.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
x2 – 2x – 15 =3D 0=
Example C. Graph y =3D –x + 2x + 15
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0172_image075.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0173.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
x2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D –3, x =3D 5=
Example C. Graph y =3D –x + 2x + 15
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0173_image076.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0174.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
x2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D –3, x =3D 5=
Example C. Graph y =3D –x + 2x + 15
(1, 16)
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0174_image077.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0174_image078.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAAP8AAAECAwIXBIJpJ91hgptQzsfusxppAWUOsiSkUQAAOw== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0174_image079.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwC5AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAC ALYAgAAAAP8AAAI3jANwmMq54GmORmfsw+xKnXEa2E1NKIVedZorKsZfC9euOaelTeojvdvYVDiW T2aMvYQ3HlBXAAA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0174_image080.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh1AAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgDQ AAYAgAAAAAAAAAI1hI+py+0Po5y02hsD3rz7D4ZXQIrmiaYqR7buC8fyTNf2jef6zve+uwoKh8RO q4hMKpeaQwEAOw== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0174_image081.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgCwAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG AK0AgAAAAAAAAAJVBBJmqMjnoEtHLVstbXhf3YXgyJFfiZ5qlrKr58bwLLa0KdevnuO3zfvtfMEi 8QhEDpPMpbPXhD6F0ir1aoxildbs1NvlbrXg8VdcTqPXZPa5DX8vCwA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0175.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
x2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D –3, x =3D 5=
Example C. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0175_image082.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0175_image083.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAAP8AAAECAwIXBIJpJ91hgptQzsfusxppAWUOsiSkUQAAOw== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0175_image084.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP9mAAECAwIYhINhG+KiznuqTWovzBdpV2kR4G0LMwIFADs= ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0175_image085.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwC5AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAC ALYAgAAAAP8AAAI3jANwmMq54GmORmfsw+xKnXEa2E1NKIVedZorKsZfC9euOaelTeojvdvYVDiW T2aMvYQ3HlBXAAA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0175_image086.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh1AAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgDQ AAYAgAAAAAAAAAI1hI+py+0Po5y02hsD3rz7D4ZXQIrmiaYqR7buC8fyTNf2jef6zve+uwoKh8RO q4hMKpeaQwEAOw== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0175_image087.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgCwAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG AK0AgAAAAAAAAAJVBBJmqMjnoEtHLVstbXhf3YXgyJFfiZ5qlrKr58bwLLa0KdevnuO3zfvtfMEi 8QhEDpPMpbPXhD6F0ir1aoxildbs1NvlbrXg8VdcTqPXZPa5DX8vCwA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
x2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D –3, x =3D 5=
Example C. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176_image088.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAIAgAAAAAAAAAIFjI+py1wAO1== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176_image089.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAAP8AAAECAwIXBIJpJ91hgptQzsfusxppAWUOsiSkUQAAOw== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176_image090.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP9mAAECAwIYhINhG+KiznuqTWovzBdpV2kR4G0LMwIFADs= ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176_image091.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAJ AAoAgQAAAAAAAP9mAAECAwIVBIJoJ93BnENyhvoupjtKeGjKEi4FADs= ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176_image092.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwC5AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAC ALYAgAAAAP8AAAI3jANwmMq54GmORmfsw+xKnXEa2E1NKIVedZorKsZfC9euOaelTeojvdvYVDiW T2aMvYQ3HlBXAAA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176_image093.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh1AAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgDQ AAYAgAAAAAAAAAI1hI+py+0Po5y02hsD3rz7D4ZXQIrmiaYqR7buC8fyTNf2jef6zve+uwoKh8RO q4hMKpeaQwEAOw== ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0176_image094.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgCwAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwAG AK0AgAAAAAAAAAJVBBJmqMjnoEtHLVstbXhf3YXgyJFfiZ5qlrKr58bwLLa0KdevnuO3zfvtfMEi 8QhEDpPMpbPXhD6F0ir1aoxildbs1NvlbrXg8VdcTqPXZPa5DX8vCwA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0177.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
x2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D –3, x =3D 5=
Example C. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
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AK0AgAAAAAAAAAJVBBJmqMjnoEtHLVstbXhf3YXgyJFfiZ5qlrKr58bwLLa0KdevnuO3zfvtfMEi 8QhEDpPMpbPXhD6F0ir1aoxildbs1NvlbrXg8VdcTqPXZPa5DX8vCwA7 ------=_NextPart_01C9B84F.9DA3E1A0 Content-Location: file:///C:/48593C93/37ConicSections-CirclesandParabolas_files/slide0178.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Conic Sections
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
2. Find a= nother point, use the y-intercept (0, c) if possible.
3. Locate the its reflection across the center line, these three = points fo= rm the tip of the parabola. Trace the parabola.
4. Set y = =3D 0 and solve to find the x intercept.
-b=
2a=
Graphs of Quadratic Equations
The vertex is at x =3D 1, y =3D 16
y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, set y =3D 0 to get x-int:
–<= /span>x2 + 2x + 15 =3D 0
x2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D –3, x =3D 5=
Example C. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
(-3, = 0)
(5, 0= )
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ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && !parent.IsFramesMode() ) || (event && (event.keyCode=3D=3D32) ) ) parent.GoToNextSld(); } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D90, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var gMainDoc=3Dnew Array(new hrefList("slide0021.htm",1,-1,1),new hrefList(= "slide0066.htm",1,-1,1),new hrefList("slide0067.htm",1,-1,1),new hrefList("= slide0068.htm",1,-1,1),new hrefList("slide0069.htm",1,-1,1),new hrefList("s= lide0070.htm",1,-1,1),new hrefList("slide0071.htm",1,-1,1),new hrefList("sl= ide0072.htm",1,-1,1),new hrefList("slide0073.htm",1,-1,1),new hrefList("sli= de0074.htm",1,-1,1),new hrefList("slide0075.htm",1,-1,1),new hrefList("slid= e0076.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("slide= 0092.htm",1,-1,1),new hrefList("slide0093.htm",1,-1,1),new hrefList("slide0= 065.htm",1,-1,1),new hrefList("slide0094.htm",1,-1,1),new hrefList("slide00= 95.htm",1,-1,1),new hrefList("slide0096.htm",1,-1,1),new hrefList("slide009= 7.htm",1,-1,1),new hrefList("slide0098.htm",1,-1,1),new hrefList("slide0035= .htm",1,-1,1),new hrefList("slide0099.htm",1,-1,1),new hrefList("slide0100.= htm",1,-1,1),new hrefList("slide0101.htm",1,-1,1),new hrefList("slide0102.h= tm",1,-1,1),new hrefList("slide0103.htm",1,-1,1),new hrefList("slide0104.ht= m",1,-1,1),new hrefList("slide0105.htm",1,-1,1),new hrefList("slide0064.htm= ",1,-1,1),new hrefList("slide0107.htm",1,-1,1),new hrefList("slide0108.htm"= ,1,-1,1),new hrefList("slide0106.htm",1,-1,1),new hrefList("slide0109.htm",= 1,-1,1),new hrefList("slide0110.htm",1,-1,1),new hrefList("slide0111.htm",1= ,-1,1),new hrefList("slide0051.htm",1,-1,1),new hrefList("slide0112.htm",1,= -1,1),new hrefList("slide0113.htm",1,-1,1),new hrefList("slide0114.htm",1,-= 1,1),new hrefList("slide0123.htm",1,-1,1),new hrefList("slide0115.htm",1,-1= ,1),new hrefList("slide0116.htm",1,-1,1),new hrefList("slide0117.htm",1,-1,= 1),new hrefList("slide0118.htm",1,-1,1),new hrefList("slide0119.htm",1,-1,1= ),new hrefList("slide0120.htm",1,-1,1),new hrefList("slide0121.htm",1,-1,1)= ,new hrefList("slide0057.htm",1,-1,1),new hrefList("slide0124.htm",1,-1,1),= new hrefList("slide0125.htm",1,-1,1),new hrefList("slide0126.htm",1,-1,1),n= ew hrefList("slide0127.htm",1,-1,1),new hrefList("slide0128.htm",1,-1,1),ne= w hrefList("slide0129.htm",1,-1,1),new hrefList("slide0130.htm",1,-1,1),new= hrefList("slide0131.htm",1,-1,1),new hrefList("slide0132.htm",1,-1,1),new = hrefList("slide0133.htm",1,-1,1),new hrefList("slide0134.htm",1,-1,1),new h= refList("slide0135.htm",1,-1,1),new hrefList("slide0136.htm",1,-1,1),new hr= efList("slide0137.htm",1,-1,1),new hrefList("slide0152.htm",1,-1,1),new hre= fList("slide0153.htm",1,-1,1),new hrefList("slide0154.htm",1,-1,1),new href= List("slide0155.htm",1,-1,1),new hrefList("slide0156.htm",1,-1,1),new hrefL= ist("slide0157.htm",1,-1,1),new hrefList("slide0158.htm",1,-1,1),new hrefLi= st("slide0159.htm",1,-1,1),new hrefList("slide0160.htm",1,-1,1),new hrefLis= t("slide0161.htm",1,-1,1),new hrefList("slide0162.htm",1,-1,1),new hrefList= ("slide0163.htm",1,-1,1),new hrefList("slide0164.htm",1,-1,1),new hrefList(= "slide0165.htm",1,-1,1),new hrefList("slide0166.htm",1,-1,1),new hrefList("= slide0167.htm",1,-1,1),new hrefList("slide0168.htm",1,-1,1),new hrefList("s= lide0169.htm",1,-1,1),new hrefList("slide0170.htm",1,-1,1),new hrefList("sl= ide0171.htm",1,-1,1),new hrefList("slide0172.htm",1,-1,1),new hrefList("sli= de0173.htm",1,-1,1),new hrefList("slide0174.htm",1,-1,1),new hrefList("slid= e0175.htm",1,-1,1),new hrefList("slide0176.htm",1,-1,1),new hrefList("slide= 0177.htm",1,-1,1),new hrefList("slide0178.htm",1,-1,1)); function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) { var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix(); function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') { href=3Dnew String(document.location.href) Start=3Dhref.indexOf('!')+1 End=3Dhref.lastIndexOf('/')+1 if (End < Start) return href.substring(0, Start) else return href.substring(0, End) } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ToggleOtlPane() { frmset=3Ddocument.all("PPTHorizAdjust") frm=3Ddocument.all("PPTOtl") if( gOtlOpen ) frmset.cols=3D"*,100%" else frmset.cols=3D"25%,*" gOtlOpen=3D!gOtlOpen frm.noResize=3D!frm.noResize UpdOtNavPane() } function ToggleNtsPane() { frmset=3Ddocument.all("PPTVertAdjust") frm=3Ddocument.all("PPTNts") if( gNtsOpen ) frmset.rows=3D"100%,*" else frmset.rows=3D"*,20%" gNtsOpen=3D!gNtsOpen UpdNtsPane() } function ClearMedia() { if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() { if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else return gCurSld } function GetNumSlds() { if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; PPTSld.location.replace(MHTMLPrefix+obj.mSldHref) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 PPTSld.location.replace(MHTMLPrefix+href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); function ImgBtn( oId,bId,w,action ) { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } function TxtBtn( oId,oeId,action,chkState ) { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b