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------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD3gAAAAUAMwAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABAAAAC0BAAAEAAAAJwH//xwAAAD7 Avn/AAAAAAAAvAIAAAAAAEAAIkFyaWFsAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABAAAAC0B AwAEAAAALgEYAAQAAAACAQEABQAAAAkCAAAAAjMAAAAyCgcAHgAdAAAAR3JhcGhzIG9mIFF1YWRy YXRpYyBFcXVhdGlvbnMABQADAAQABAAEAAQAAgAFAAIAAgAFAAQABQAEAAMABAACAAIABAACAAUA BAAEAAQAAgADAAQABAAEAAQAAAAuAQAAHAAAAPsCEAAHAAAAAAC8AgAAAAABAgIiU3lzdGVtAAAA AAAAAAAAABgAAAABAAAAcDcVAOQEAAAEAAAALQEEAAQAAADwAQMAAwAAAAAA ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0117.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x.
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0118.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x.
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0119.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x. Suppose we know another point on the parabola,
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0120.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x. Suppose we know another point on the parabola,
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0121.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x. Suppose we know another point on the parabola, then the reflection of the point across the center line is also on the pa= rabola.
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0122.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x. Suppose we know another point on the parabola, then the reflection of the point across the center line is also on the pa= rabola.
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x. Suppose we know another point on the parabola, then the reflection of the point across the center line is also on the pa= rabola. There is exactly one parabola that goes through these three po= ints.
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0124.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Each parabola has a vertex and the center line that contains the verte= x. Suppose we know another point on the parabola, then the reflection of the point across the center line is also on the pa= rabola. There is exactly one parabola that goes through these three po= ints.
The graphs of the equa= tions of the form
y =3D ax2 + bx + c and x =3D ay2 + bx + c
are parabolas.<= /div>
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0116.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
When graphing parabolas, we must also give the x-intercepts = <= span lang=3DEN-US style=3D'font-size:133%;mso-fareast-language:ZH-CN'>and the y-intercept.
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0125.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is obt= ained by setting x =3D 0 and solve for y.
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is obt= ained by setting x =3D 0 and solve for y.
The x-intercept is obt= ained by setting y =3D 0 and solve for x.
Graphs of Quadratic Equations
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0127.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is obt= ained by setting x =3D 0 and solve for y.
The x-intercept is obt= ained by setting y =3D 0 and solve for x.
Graphs of Quadratic Equations
The graph= s of y =3D ax2 + bx =3D c are up-down parabolas.<= /span>
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0129.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is obt= ained by setting x =3D 0 and solve for y.
The x-intercept is obt= ained by setting y =3D 0 and solve for x.
Graphs of Quadratic Equations
The graphs of y =3D ax= 2 + bx =3D c are up-down parabolas.
If a > 0, the parab= ola opens up.
a > 0
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When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is obt= ained by setting x =3D 0 and solve for y.
The x-intercept is obt= ained by setting y =3D 0 and solve for x.
Graphs of Quadratic Equations
The graphs of y =3D ax= 2 + bx =3D c are up-down parabolas.
If a > 0, the parab= ola opens up.
If a < 0, the parab= ola opens down.
a > 0
a < 0
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When graphing parabola= s, we must also give the x-intercepts and the y-intercept. &= #13;
The y-intercept is obt= ained by setting x =3D 0 and solve for y.
The x-intercept is obt= ained by setting y =3D 0 and solve for x.
Graphs of Quadratic Equations
The graphs of y =3D ax= 2 + bx =3D c are up-down parabolas.
If a > 0, the parab= ola opens up.
If a < 0, the parab= ola opens down.
a > 0
a < 0
= Vertex Formula (up-down parabolas) The x-coordinate of <= /span>
the vertex of the parabola y = =3D ax + bx + c is at x =3D      .<= span lang=3DEN-US style=3D'font-family:\5B8B\4F53;mso-ascii-font-family:Tahoma; mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-family:Tahoma;font-size: 133%;mso-fareast-language:ZH-CN;mso-special-format:lastCR;display:none'>&#= 13;
-b=
2a=
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Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + bx + c.
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0132.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + bx + c.
<= span style=3D'font-size:133%'>1.Set x =3D       in = the equation to find the vertex.
-b=
2a=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0132_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0133.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0133_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0134.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0134_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0135.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0135_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0136.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
Example A. Graph y =3D –x + 2x + 15
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0136_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0137.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
The vertex is at x =3D       =3D= 1
Example A. Graph y =3D –x + 2x + 15
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0137_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAb AAIAgAAAAAAAAAIGjI+py90FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0137_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0138.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
The vertex is at x =3D       =3D= 1ày =3D 16.
Example A. Graph y =3D –x + 2x + 15
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0138_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAb AAIAgAAAAAAAAAIGjI+py90FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0138_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0139.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
The vertex is at x =3D       =3D= 1ày =3D 16.
Example A. Graph y =3D –x + 2x + 15
(1, 16)
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0139_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAoAgQAAAAAAAP8AAAECAwIWhBF3EcIrYkxNSmZvzTi7bVHcwjxAAQA7 ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0139_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhAwC5AHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAB ALYAgAAAAP8AAAIgTGCAmrl43IH0tYkjZprxmoGfNG4UeZqXl7Kr1cEiVAAAOw== ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0139_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgCwAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAgAF AK4AgAAAAAAAAAJIBGKGGtv44lPp1EUTtvr6DmYiN27mV6Lkeoas2qZu/M7wbefyXvP0j/MFe0Sg rjg0Co9KJDMJfUqXVGe1iY1etdZudurlfpcFADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0139_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAb AAIAgAAAAAAAAAIGjI+py90FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0139_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX AAIAgAAAAAAAAAIGjI+pyx0FADs= ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0139_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhsAAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgCt AAYAgAAAAAAAAAIyhI+py+0Po5y0ymCz3rz7H4TfSJbmmYQqoLbuC8fyTNf2jef67qL+DwwaWsKi 8ZgRHQoAOw== ------=_NextPart_01C8F4FF.90BD6BF0 Content-Location: file:///C:/48593C93/5Parabolas_files/slide0140.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Graphs of Quadratic Equations
The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Example A. Graph y =3D –x + 2x + 15
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
(1, 16)
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Example A. Graph y =3D –x + 2x + 15
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
(1, 16)
(0, 1= 5)
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15).
Example A. Graph y =3D –x + 2x + 15
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
(1, 16)
(0, 1= 5)
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15).
Example A. Graph y =3D –x + 2x + 15
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
(1, 16)
(0, 1= 5)
(2, 1= 5)
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw,
Example A. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, se= t y =3D 0 to get x-int:
Example A. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, se= t y =3D 0 to get x-int:
–x= 2 + 2x + 15 =3D 0
Example A. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, se= t y =3D 0 to get x-int:
–x= 2 + 2x + 15 =3D 0
x= 2 – 2x – 15 =3D 0=
Example A. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, se= t y =3D 0 to get x-int:
–x= 2 + 2x + 15 =3D 0
x= 2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D &#= 8211;3, x =3D 5
Example A. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
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The vertex is at x =3D       =3D= 1ày =3D 16.
The y-intercept is at (0, 15)
Plot its reflection (2, 15)
Draw, se= t y =3D 0 to get x-int:
–x= 2 + 2x + 15 =3D 0
x= 2 – 2x – 15 =3D 0
(x + 3)(x – 5) =3D 0
x =3D &#= 8211;3, x =3D 5
Example A. Graph y =3D –x + 2x + 15
(1, 16)
(0, 1= 5)
(2, 1= 5)
(-3, = 0)
(5, 0= )
–(2)=
 2(–1)
Graphs of Quadratic Equations
Following= are the steps to graph the parabola y =3D ax2 + 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=
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