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Transformations of Quadratic Functions

Total questions: 15

Worksheet time: 37mins

Name
Class
Date
1.
Which transformation transforms the graph of
f(x) = x2 to the graph of
g(x) = (x + 4)2?
a)
a vertical translation 4 units up
b)
a vertical translation 4 units down
c)
a horizontal translation 4 units to the left
d)
a horizontal translation 4 units to the right
2.
How did we transform from the parent function?
g(x) = -1/5(x - 1)2 + 7
a)
reflection, vertical compression, horizontal right, vertical up
b)
vertical compression, horizontal shift left, vertical shift up
c)
reflection, horizontal shift right, vertical shift down
d)
no changes were made to y = x2
3.
In the equation f(x)=5(x+3)2-10 what does the 5 do?
a)
Vertical stretch by 5
b)
Horizontal compress by 5
c)
Reflect
d)
Move up 5
4.
What is the vertical shift of this equation?
f(x) = -(x + 3)2 - 5
a)
left 5
b)
right 5
c)
up 5
d)
down 5
5.
Does the graph of this equation open up or down? 
f(x) = -(x + 3)2 - 5
a)
up
b)
down
6.
If the blue graph is
f(x) = x2 
then the red must be...
a)
g(x) = x2 - 5
b)
g(x) = x2 + 5
c)
g(x) = (x - 5)2
d)
g(x) = (x + 5)2
7.
What transformations have occurred? 
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
8.
Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)2
a)
horizontal shift left 7 units
b)
horizontal shift right 7 units
c)
vertical shift up 7 units
d)
vertical shift down 7 units
9.

Which of the following describes the transformations done to the quadratic parent function of f(x) = x2 to obtain g(x) = 2x2 + 4 ?

a)

Vertical Stretch by a factor of 2 and vertical shift up 4 units

b)

Vertical Compress by a factor 2 and vertical shift up 4

c)

Vertical Stretch by a factor of 2 and horizontal shift left 4 units

d)

Vertical Compress by a factor of 2 and horizontal shift right 4 units

10.

What is the equation of the quadratic function obtained from vertically compressing the parent function by 3/5 and then shifted up 8 units?

a)

f(x)= 3/5(x-8)2

b)

f(x)=3/5x2+8

c)

f(x)=x2

d)

f(x)=3/5x2-8

11.
What is the equation of the quadratic function obtained from horizontally shifting the parent function 17 units left and then reflecting across the x-axis?
a)
f(x)= -x2-17
b)
f(x)= -(x-17)2
c)
f(x)= -(x+17)2
d)
f(x)= -x2+17
12.
What is the equation of the quadratic function obtained from vertically stretching the parent function by a factor of 2 and then vertically shifting up 3 units?
a)
f(x)= 2(x-3)2
b)
f(x)= 2(x+3)2
c)
f(x)= 2x2+3
d)
f(x)= (x-2)2+3
13.

What is the equation of the quadratic function obtained from vertically compressing the parent function by a factor of 0.5 and then reflecting across the x-axis?

a)

f(x)= 0.5x2

b)

f(x)= -0.5x2

c)

f(x)= -(x-0.5)2

d)

f(x)= x2+0.5

14.
Which quadratic function is represented by the graph?
a)
y = 2(x - 4)2 + 5
b)
y = 2(x + 4)2 + 5
c)
y = -2(x - 4)2 + 5
d)
y = -2(x + 4)2 + 5
15.
What is the horizontal shift of this equation?
y = -(x + 3)2 - 5
a)
left 3
b)
right 3
c)
left 5
d)
right 5