; Solving Quadratic Functions by Graphing
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# Solving Quadratic Functions by Graphing

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• pg 1
```									Investigating Graphs
of
Objectives

• You will be able to describe how the
values of the coefficients of a
quadratic function affect the graph.

• You will be able recognize the graph
of a quadratic function by it’s
equation.

Algebra I Honors   Graphing Quadratic Functions   Pankowski
Review
How to graph a quadratic function by
hand:
1. Find the x-coordinate of the vertex: -
b/(2a).
2. Make a table of values, using x-values to
the left and right of the vertex.
3. Plot the points and connect them with a
smooth curve to form a parabola.

Algebra I Honors     Graphing Quadratic Functions   Pankowski
Example:
y  x  2x  3
2

a=     1
x-coordinate of vertex  (2) /(2 *1)                  b=    -2
 2 /2                   c=    -3
1

y-coordinate of vertex  12  2(1)  3
 1 2  3

 1 3             Vertex    (1,4)
 4

Algebra I Honors        Graphing Quadratic Functions         Pankowski
y  x  2x  3
2

Pick values to left and right of Vertex (equidistant
from vertex)
-The vertex is located at (1,-4).

-One unit to the right

and left of x=1 are x=0
and x=2.

-Two units to the right
and left of x=1 are x=3
and x=-1.
-Make a table by
substituting these x-values
into your function to find
their corresponding y-
values.
Algebra I Honors           Graphing Quadratic Functions   Pankowski
y  x  2x  3
2

x 1                        x2                        x0
y  12  2(1)  3           y  2 2  2(2)  3         y  0 2  2(0)  3
y  1 2  3                y 443                   y  00 3
y  1 3                   y  0 3                   y  0 3

y  4                      y  3                     y  3
Vertex  (1,4)             B  (2,3)                 C  (0,3)

x  1                      x3
        y  (1) 2  2(1) 
3        y  32  2(3)  3 
y  1 2  3                y  96 3
y  3 3                     y  3 3
y0                          y0
D  (1,0)                   E  (3,0)

Algebra I Honors              Graphing Quadratic Functions              Pankowski
Table of Values
Point                    X                  Y

Vertex                     1                  -4

B                  2                  -3

C                  0                  -3

D                 -1                  0

E                  3                  0

Algebra I Honors          Graphing Quadratic Functions        Pankowski
Plot the Points and
Connect a Smooth Curve

Algebra I Honors    Graphing Quadratic Functions   Pankowski
Investigation
• Open your laptop

• Open the file on your desktop labeled
“Multimedia1a_Dynamic_Worksheet_EHP.h
tml”

• Answer the questions on the worksheet by
investigating using the sliders
Algebra I Honors     Graphing Quadratic Functions   Pankowski

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