Algebra 3 Solving Quadratic Equations Worksheet - Brunel University Page 12
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13Sketching graphs of quadratic function
As mentioned above the completed square form can be used for sketch-
2
A(x + B)
+ C
ing the graph of any quadratic function
. We start
2
y = x
with the graph of elementary function
. Then we need
• A
A > 1
A < 1
effect -
stretch
(
) or
compress
(
) vertically
• B
B < 0
B > 0
effect -
shift to the right
(
) or
left
(
)
• C
C < 0
C > 0
effect-
shift down
(
) or
up
(
)
Example
2
y = 2(x + 3)
41
To sketch the graph
we start with the graph of
2
y = x
A = 2
B = 3
C =
41
. We have
,
and
200
150
2
2 x
y
A = 2 > 1
100
2
x
2
y = x
stretch the graph
vertically
50
0
-10
-5
0
5
10
x
200
150
2
2 x
2
2 x 3
y
B = 3
100
2
y = 2x
shift the graph
to the left
50
0
-10
-5
0
5
10
x
12
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