Transformations Of Quadratic Functions Worksheet Page 2
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1
2
3Name: _____________________________________________________________
Date: _________________________
Period: ______
6-3
From Geometry: A translation is a rigid motion that slides a figure on the coordinate plane without
changing its size or shape.
Translations of Quadratic Graphs
Recall the general look of a quadratic graph
Consider �� = ��
2
The general equation of an absolute value graph is �� = �� ( �� − �� )
��
+ ��
��: Tells you if the parabola opens up or down
+ ��
opens up
−��
opens down
Larger ��, narrower graph
Smaller ��, wider graph
ℎ: Horizontal Translation. Shifts the parabola left or right
�� + ℎ shifts left
�� − ℎ shifts right
��: Vertical Translation: Shifts the parabola up or down
shifts up
+ ��
shifts down
− ��
Identify the vertex & describe the shifts of each parabola below
1) �� = ( �� + 5 )
2
2) �� = ( �� − 1 )
2
– 6
+ 7
1
3) �� = 2 ( �� − 5 )
2
4) �� =
2
+ 2
( �� + 3 )
− 6
2
5) Write a quadratic equation that transforms the graph of �� = 2 ( �� + 1 )
+ 3 so that it is:
2
a) 2 units up
b) 3 units down
c) 2 units to the left
d) 3 units to the right
e) narrower
f) wider
g) opening in the opposite direction
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