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Quadratic Transformations

Total questions: 50

Worksheet time: 1hrs 19mins

Name
Class
Date
1.

Choose the equation of the quadratic function that is translated 6 units up, 2 units right, and is vertically stretched by a factor of 3 from the parent function.

a)

f(x) = 3(x - 2)2+6

b)

f(x) = 6(x + 2)2+3

c)

f(x) = 3(x + 2)2 + 6

d)

f(x) = 6(x - 2)2-3

2.

Choose the equation of the quadratic function that is reflected over the x-axis and translated down 3.

a)

f(x) = -x2 + 3

b)

f(x) = -x2 -3

c)

f(x) = -(x-3)2

d)

f(x) = -(x+3)2

3.

Use transformations to identify the equation of the graph shown.

a)

f(x) = (x - 5)2 - 2

b)

f(x) = (x + 5)2 - 2

c)

f(x) = (x - 5)2 + 2

d)

f(x) = (x + 5)2 + 2

4.

Use transformations to identify the equation of the graph shown.

a)

f(x) = (x + 3)2 - 8

b)

f(x) = 3(x + 3)2 - 8

c)

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

d)

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

5.
Which transformation will occur if f(x) = x2 is replaced with 2⋅f(x)?
a)

Wider

b)

Narrower

c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
6.
Which transformation will occur if f(x) = x2 is replaced with f(x) + 2?
a)

Translation left 2 units

b)

Narrower

c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
7.
Which transformation will occur if f(x) = x2 is replaced with -f(x)?
a)
Nothing happens, it stays the same.
b)

Narrower

c)
Vertical translation up by 2 units.
d)
Reflection across the x-axis.
8.
f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)
a)
g(x)=f(x - 3)
b)
g(x)=f(x) - 3
c)
g(x)=f(x) + 3
d)
g(x)=3f(x)
9.
What is the equation of the quadratic function obtained from vertically shrinking/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
10.
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
11.
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
12.
What is the equation of the quadratic function obtained from vertically shrinking/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
13.
Match the equation to its description.
a)
Right 2 and up 2
b)
Left 2 and up 2
c)
Right 2 and down 2
d)
Left 2 and down 2
14.
In the graph of the function y=x², which describes a vertical shift in the parent function up 5 units?
a)
y = x2 - 5
b)
y = x2 + 5
c)
y = (x - 5)2
d)
y = (x + 5)2
15.
If the blue 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
16.
If the blue is f(x)=x2, the red must be
a)
g(x)=(x+3)2
b)
g(x)=(x-3)2
c)
g(x)=x2+3
d)
g(x)=x2-2
17.
Identify the transformation from the graph of f(x)=x2 to the graph g(x)= -(x+5)2 
a)
shifted up five units
reflection in x-axis
b)
shifted down five units
reflection in x-axis
c)
shifted left 5 units
reflection x-axis
d)
shifted right 5 units
reflection x-axis
18.
Identify the transformations. 
a)
horizontal shift to the left 2 and vertical stretch by a factor of 3
b)
horizontal shift to the right 2 and vertical stretch by a factor of 3
c)
horizontal shift to the right 2 and vertical shrink by a factor of 3
d)
horizontal shift to the left 2 and vertical shrink by a factor of 3
19.
Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10
a)
Reflect over y-axis
Shifted down 10 units
Shifted left 6 units
b)
Reflect over x-axis
Shifted up 10 units
Shifted left 6 units
c)
Reflect over y-axis
Shifted up 10 units
Shifted right 6 units
d)
Reflect over x-axis
Shifted down 10 units
Shifted left 6 units
20.

What is the vertex?

a)

(3, 1)

b)

(0, 1)

c)

(1, 3)

d)

No vertex

21.
If the blue 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
22.
 f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)
a)
g(x)=2f(x)
b)
g(x)=0.5f(x)
c)
g(x)=f(x) + 2
d)
g(x)=f(x + 2)
23.
f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)
a)
g(x)=f(x + 3)
b)
g(x)=f(x - 3)
c)
g(x)=f(x) + 3
d)
g(x)=f(x) - 2
24.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 6

b)

y = x2 + 6

c)

y = ( x - 6 )2

d)

y = ( x + 6 )2

25.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 5

b)

y = x2 + 5

c)

y = ( x - 5 )2

d)

y = ( x + 5 )2

26.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 1

b)

y = x2 + 1

c)

y = ( x - 1 )2

d)

y = ( x + 1 )2

27.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 5

b)

y = x2 + 5

c)

y = ( x - 5 )2

d)

y = ( x + 5 )2

28.
#1. 2f(x)
a)
vertical compression
b)
vertical stretch
c)
horizontal compression
d)
horizontal stretch
29.
Who is Harry Potter's best friend?
a)
Draco Malfoy
b)
Cedric Diggory
c)
Ronald Weasley
d)
Seamus Finnigan
30.
What is the domain of the graph?
a)
y≥1
b)
x ≥ 1
c)
All real numbers
d)
none of these
31.
What is the proper domain?
a)
x≥0
b)
y≥0
c)
All real numbers
d)
{0, 1, 2, 3, 4,...}
32.
What is the range?
a)
-3 < y ≤ 3
b)
-4 ≤ y < 5
c)
-4 ≤ y ≤ 5
d)
-3 < y ≤ 3
33.
The vertex of the quadratic function f(x) in the picture is (-4, 5). If g(x) = f(x + 2) , what is the vertex of g(x)?
a)
(-2, 5)
b)
(-6, 5)
c)
(-4, 3)
d)
(-4, 7)
34.
Describe the transformations of f(x) when compared to the parent function.
f(x)=x2+5
a)
horizontal shift right 5 units
b)
horizontal shift left 5 units
c)
vertical shift up 5 units
d)
vertical shift down 5 units
35.
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
36.
In the equation f(x)=5(x+3)2-10 what effect does the 5 do when compared to the parent function?
a)
Vertical stretch by a factor of 5
b)
Vertical shrink/compress by a factor of 5
c)
Reflect over x-axis
d)
Vertical shift up 5 units
37.
Which transformation transforms the graph of
f(x) = x2 to the graph of g(x) = (x + 4)2?
a)
a vertical shift 4 units up
b)
a vertical shift 4 units down
c)
a horizontal shift 4 units to the left
d)
a horizontal shift 4 units to the right
38.

Gracie's service club is raising money by wrapping presents in the mall. The function f(x) = 3x describes the amount of money, in dollars, the club will earn for wrapping x presents. They only have enough wrapping paper to wrap 1000 presents. Which best represents the domain?

a)

1000 ≤ x ≤ 0

b)

x ≥ 1000

c)

0 ≤ x ≤ 1000

d)

x ≤ 3000

39.
In an exponential function, what does the 'a' represent? 
a)
SLOPE
b)
RATE OF CHANGE
c)
Y-INTERCEPT
d)
COMMON RATIO
40.
The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?
a)
.08
b)
1.08
c)
.92
d)
8
41.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
42.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
a)
Growth
b)
Decay
43.
Find the slope of the line that passes through the points (2, 4) and (6, 12)
a)
1/2
b)
-1/2
c)
2
d)
-2
44.
What direction is an undefined slope?
a)
horizontal
b)
vertical
45.
Is this point a max or min?
a)
max
b)
min
46.
Is this mapping a function or not a function? 
a)
Function
b)
Not a Function 
47.
Given f(x) = -4x - 10 and f(x) = 10. Find x
a)
x = -5
b)
x = 5
c)
x = -50
d)
x = 30
48.
For the function f(x) = -3(x-1) find f(0).
a)
0
b)
-3
c)
3
d)
-1
49.
Name the x-intercept(s)?
a)
0
b)
4
c)
2
d)
0 and 4
50.
What is the x- intercept of the line?
a)
(0,-2)
b)
(0,-1)
c)
(-1,0)
d)
(-2,0)

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