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Graphs of Quadratic Equations
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
We start w= ith an example of a graph gives the general shape of the graphs of = 2nd (quadratic) degree equations.
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
We start w= ith an example of a graph gives the general shape of the graphs of = 2nd (quadratic) degree equations.
Example A.  Graph y =3D –x2
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
We start w= ith an example of a graph gives the general shape of the graphs of = 2nd (quadratic) degree equations.
Make a ta= ble
Example A.  Graph y =3D –x2
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0099.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
 x       = 3;
-4    
-3     
-2     
-1     
 0       
 1       = 3;
 2       = 3;
 3       = 3;
 4     
Graphs of Quadratic Equations
We start w= ith an example of a graph gives the general shape of the graphs of = 2nd (quadratic) degree equations.
Make a ta= ble
Example A.  Graph y =3D –x2
 y
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0101.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
 x       = 3;
-4    
-3     
-2     
-1     
 0       
 1       = 3;
 2       = 3;
 3       = 3;
 4     
Graphs of Quadratic Equations
We start w= ith an example of a graph gives the general shape of the graphs of = 2nd (quadratic) degree equations.
Make a ta= ble
Example A.  Graph y =3D –x2
 y
-16 =
-9 <= /span>
-4 <= /span>
-1 <= /span>
 0
-1 <= /span>
-4 <= /span>
-9 <= /span>
-16
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
We start w= ith an example of a graph gives the general shape of the graphs of = 2nd (quadratic) degree equations.
Make a ta= ble
Example A.  Graph y =3D –x2
 x       = 3;
-4    
-3     
-2     
-1     
 0       
 1       = 3;
 2       = 3;
 3       = 3;
 4     
 y
-16 =
-9 <= /span>
-4 <= /span>
-1 <= /span>
 0
-1 <= /span>
-4 <= /span>
-9 <= /span>
-16
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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
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0102.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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. 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0103.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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>
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0039.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0105.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example B. Graph y =3D x – 4x – 12
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0106.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0107.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0108.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0120.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0109.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
Note the y values are symmetric around t= he vertex just as the points.
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0110.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
Note the y values are symmetric around t= he vertex just as the points. (If they are not, check = your calculation.)   
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0111.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
Note the y values are symmetric around t= he vertex just as the points. (If they are not, check = your calculation.)   
(2, -16)
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0118.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
Note the y values are symmetric around t= he vertex just as the points. (If they are not, check = your calculation.)   
(2, -16)
(3, -= 15)
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0119.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
Note the y values are symmetric around t= he vertex just as the points. (If they are not, check = your calculation.)   
(2, -16)
(4, -= 12)
(3, -= 15)
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0112.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
Note the y values are symmetric around t= he vertex just as the points. (If they are not, check = your calculation.)   
(2, -16)
(4, -= 12)
(3, -= 15)
(1, -= 15)
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0113.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
Make a table centered at x =3D 2.=
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
Note the y values are symmetric around t= he vertex just as the points. (If they are not, check = your calculation.)   
(2, -16)
(0, -= 12)
(4, -= 12)
(3, -= 15)
(1, -= 15)
–12    
–15 
–16
–15
–12
 
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0078.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
Graphs of Quadratic Equations
Example = B. Graph y =3D x – 4x – 12 <= /div>
Vertex: set  x =3D         =3D 2
–(–4)
 2(1)
(2, -16)
(0, -= 12)
(4, -= 12)
Make a table centered at x =3D 2.
Note the y values are symmetric around t= he vertex just as the points. (If they are not, check = your calculation.)   
(3, -= 15)
(1, -= 15)
One way to graph a parabola is to make a table around the = vertex so= the points will be plotted symmetrically.
 x       y&#= 13;
 0        = ; 
 1       = 3;
 2    
 3    
 4    
 
–12    
–15 
–16
–15
–12
 
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Graphs of Quadratic Equations
When graphing parabolas, we must also give the x-intercepts = = and the y-intercept.
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0121.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0122.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0124.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0125.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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.
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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.
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0128.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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.
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0129.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
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.
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0051.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(2= nd way) To graph a parabola y =3D ax<= /span>2 + bx + c.
Graphs of Quadratic Equations
------=_NextPart_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0130.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0131.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0132.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0133.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0134.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0135.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(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_01C96703.57F9EED0 Content-Location: file:///C:/09764A33/4TheGraphsofQuadraticEquations_files/slide0136.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Graphs of Quadratic Equation
(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
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