wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

dilations of quadratic functions

Total questions: 80

Worksheet time: 5hrs 43mins

Name
Class
Date
1.
The graph of a quadratic function is called a
a)
Parabola
b)
Vertex
c)
Axis of Symmetry 
d)
Vertex Form
2.
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
3.
. 
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
4.

Which of the following equations represents f(x)=x2f\left(x\right)=x^2  after being transformed by 3 to the right and down 10

a)

f(x)= x + 13

b)

f(x) = (x + 10)2 + 3

c)

f(x) = (x - 3)2 - 10

d)

f(x) = x - 13

5.

Match the equation to its description

f(x)=(x−2)2+2f\left(x\right)=\left(x-2\right)^2+2  

a)

Right 2 and up 2

b)

Right 2 and down 2

c)

Left 2 and up 2

d)

Left 2 and down 2

6.

f(x)=(x+5)2−4f\left(x\right)=\left(x+5\right)^2-4  

Describe this translation:

a)

Right 5 and up 4

b)

Left 5 and down 4 

c)

down 5 and right 4 

d)

up 5 and left 4 

7.

Given f(x) = (x-3)2 - 5.  What transformations took place from the original function f(x)?

a)
Left 3 and up 5
b)

Right 3 and up 5

c)
Left 3 and down 5
d)

Right 3 and down 5

8.

Which transformation transforms the graph of f(x) = x2 to the graph of g(x) = (x + 2)2+9

a)

left 2 and down 9

b)

right 2 and up five

c)

left 2 and up 9

d)

left 9 and up 2

9.

Which of the following equations represents f(x)=x2f\left(x\right)=x^2  after being transformed by 4 to the left and up 7

a)

f(x)= x + 4

b)

f(x) = (x + 4)2 + 7

c)

f(x) = (x + 7)2 - 4

d)

f(x) = x - 7

10.
What equation represents the quadratic function?
a)
y = (x - 4)2
b)
y = (x + 4)2
c)
y = x2 - 4
d)
y = x2 + 4
11.
What equation represents the quadratic function?
a)
y = (x - 4)2
b)
y = (x + 4)2
c)
y = x2 - 4
d)
y = x2 + 4
12.
What equation represents the quadratic function?
a)
y = (x - 8)2
b)
y = (x + 8)2
c)
y = x2 - 8
d)
y = x2 + 8
13.
What equation represents the quadratic function?
a)
y = (x - 5)2 - 3
b)
y = (x - 5)2 + 3
c)
y = (x + 5)2 - 3
d)
y = (x - 3)2 - 5
14.
What equation represents the quadratic function?
a)
y = (x - 7)2 - 2
b)
y = (x + 7)2 + 2
c)
y = (x + 7)2 - 2
d)
y = (x + 2)2 + 7
15.
What equation represents the quadratic function?
a)
y = -(x - 5)2 
b)
y = -x2 + 5
c)
y = x2 - 5
d)
y = (x - 5)2 
16.
What equation represents the quadratic function?
a)
y = -(x - 6)2 - 3
b)
y = -(x - 6)2 + 3
c)
y = -(x + 6)2 - 3
d)
y = -(x + 6)2 + 3 
17.
What equation represents the quadratic function?
a)
y = (x - 4)2 + 1
b)
y = (x + 1)2 - 4
c)
y = (x - 4)2 - 1
d)
y = (x - 1)2 - 4 
18.

What change does a Translation Cause?

a)

a shift up, down, left, or right

b)

a reflection

c)

a compression

d)

a stretch

19.
Which equation below is a quadratic function translated up 5 units?
a)
y = x2 + 5
b)
y = (x + 5)2
c)
y = 5x2
d)
y = -x2 - 5
20.
The graph of a quadratic function is called a
a)
Parabola
b)
Vertex
c)
Axis of Symmetry 
d)
Vertex Form
21.
Name the parent function.
a)
quadratic
b)
cubic
c)
square root
d)
logarithmic
22.
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
23.
Which equation below is a quadratic function translated left 4 units?
a)
y = x2 + 4
b)
y = (x + 4)2
c)
y = (x - 4)2
d)
y = 4x2
24.
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)
25.
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
26.

Which equation below is a quadratic function translated up 3 units?

a)

y = x2 + 3

b)

y = (x + 3)2

c)

y = 3x2

d)

y = -x2 - 3

27.

Which of the following quadratics has a range of all real numbers less than or equal to 4?

a)

b)

c)

d)

28.
Which equation below is a quadratic function translated up 5 units?
a)
y = x2 + 5
b)
y = (x + 5)2
c)
y = 5x2
d)
y = -x2 - 5
29.
What equation represents the quadratic function?
a)
y = (x - 5)2 - 3
b)
y = (x - 5)2 + 3
c)
y = (x + 5)2 - 3
d)
y = (x - 3)2 - 5
30.
What is the domain of the function?
*Hint: Domain is the set of all x-values included in the function.
a)
x≥3
b)
x≤3
c)
All real numbers
d)
-1≤x≤5
31.

Which graph best represents a function with a range of all real numbers greater than or equal to -6?

a)
b)
c)
d)
32.

Which graph represents a function with a domain of all real numbers greater than or equal to -7 and less than 2?

a)
b)
c)
d)
33.

Determine the domain and range of the function.

a)

Domain: all real numbers.

Range: all real numbers less than or equal to 1.

b)

Domain: all real numbers.

Range: all real numbers less than or equal to 2.

c)

Domain: all real numbers less than or equal to 1.

Range: all real numbers.

d)

Domain: all numbers between 1 and 3.

Range: all real numbers less than or equal to 1.

34.

What is the vertex of the quadratic function shown?

a)

(5, 5)

b)

(-5, -5)

c)

(2, 0)

d)

(0, -2.5)

35.
Using the Axis of Symmetry formula, find the coordinates of the vertex.
-x2 + 4x - 6
a)
(2, -2)
b)
(-2, 2)
c)
(0, 2)
d)
(0, -2)
36.
Using the Axis of Symmetry formula, find the coordinates of the vertex.
-3x2 + 12x - 7
a)
(5, 2)
b)
(-2, 5)
c)
(2, 5)
d)
(-5, 2)
37.

Compare the function y = 5x2 to the parent function y = x2. How did the parabola change?

a)

A vertical compression made the parabola wider.

b)

A vertical stretch made the parabola narrower.

c)

The parabola shifted horizontally

d)

The parabola shifted vertically

38.

Compare the function y = -9x2 to the parent function y = x2. How did the parabola change?

a)

A vertical compression made the parabola wider.

b)

A vertical stretch made the parabola narrower.

c)

The parabola shifted horizontally

d)

The parabola shifted vertically

39.

Compare the function y = 3/4x2 to the parent function y = x2. How did the parabola change?

a)

A vertical compression made the parabola wider.

b)

A vertical stretch made the parabola narrower.

c)

The parabola shifted horizontally

d)

The parabola shifted vertically

40.

Select the equation of the quadratic function (parabola):

a)

y = x2 - 8

b)

y = x2 + 8

c)

y = ( x - 8 )2

d)

y = ( x + 8 )2

41.
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
42.

If the function f(x) = x2 is changed so that a new function is created, g(x) = 5x2, how does g(x) compare to f(x)?

a)

The graph of g(x) is wider than the graph of f(x)

b)

The graph of g(x) is narrower than the graph of f(x)

c)

The graph of g(x) is shifted 5 units up above f(x)

d)

The graph of g(x) is shifted 5 units down below f(x)

43.

If the function f(x) = x2 is changed so that a new function is created, r(x) = 1/3nf(x), how does r(x) compare to f(x)?

a)

The graph of r(x) is wider than the graph of f(x)

b)

The graph of r(x) is narrower than the graph of f(x)

c)

The graph of r(x) is shifted 5 units up above f(x)

d)

The graph of r(x) is shifted 5 units down below f(x)

44.

Which of the following shows a vertical compression of the parent function f(x)=x2?

a)

y = 2x2

b)

y = 3/5x2

c)

y = -4x2

d)

y = -x2

45.

Does the equation vertically stretch or compress?

f(x)= 2x2f\left(x\right)=\ 2x^2  
*Always compare to the parent function (graph first)*

a)

vertically stretch

b)

vertically compress

c)

horizontally shift 4 units left

d)

horizontally shift 4 units right

46.
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
47.

Describe the transformations from the original parent function f(x) = x2.

g(x) = 5x2 + 2

a)

Vertical Compression of 5

Translated Down 2

b)

Vertical Compression of 5

Translated Up 2

c)

Vertical Stretch of 5

Translated Up 2

d)

Vertical Shrink of 5

Translated Down 2

48.

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

49.

How did we transform from f(x) =x2  to g(x) = 3x2

a)

vertical shift down

b)

vertical stretch

c)
horizontal stretch
d)

vertical compression

50.
a)
g(x)=2x2
b)
g(x)=0.5x2
c)
g(x)=x2+2
d)
g(x)=(x+2)2
51.

How did we transform from f(x) =x2  to g(x) = 3x2

a)

vertical shift down

b)

vertical stretch

c)
horizontal stretch
d)

vertical compression

52.

Determine the vertex from the following equation: −(x+1)2−1-\left(x+1\right)^2-1  

a)

Vertex: (1,-1)

b)

Vertex: (-1, 1)

c)

Vertex: (-1, -1)

d)

Vertex: (1, 1)

53.

Determine the vertex from the following equation: 12(x+4)2+1\frac{1}{2}\left(x+4\right)^2+1  

a)

Vertex: (-4, 1)

b)

Vertex: (-4, -1)

c)

Vertex: (4, 1)

d)

Vertex: (4, -1)

54.

Determine the axis of symmetry of the following equation: −2(x+2)2+3-2\left(x+2\right)^2+3  

a)

A. O. S: 3

b)

A. O. S: -2

c)

A. O. S: 2

d)

A. O. S: 1

55.

Determine the axis of symmetry of the following equation: (x−3)2+5\left(x-3\right)^2+5  

a)

A. O. S: 1

b)

A. O. S: -3

c)

A. O. S: 3

d)

A. O. S: 5

56.

Determine if the parabola has a maximum or minimum, if it opens up (+) then it will have a minimum, if it opens down (-) then it will have a maximum. 3(x+3)2−23\left(x+3\right)^2-2  

a)

Maximum

b)

Minimum

57.

Determine if the following equation has a maximum or minimum: −(x−2)2+7-\left(x-2\right)^2+7  

a)

Maximum

b)

Minimum

58.

What is a quadratic funtion in the form of f(x)=a(x−h)2+kf\left(x\right)=a\left(x-h\right)^2+k  called?

a)

Factored Form

b)

Standard Form

c)

Vertex Form

59.

What is the vertex of the equation

y=(x−3)2+5y=\left(x-3\right)^2+5  

a)

(-3, 5)

b)

(3, 5)

c)

(-3, -5)

d)

(3, -5)

60.

What is the vertex of the equation

y=(x+7)2+3y=\left(x+7\right)^2+3  

a)

(7, 3)

b)

(7, -3)

c)

(-7, 3)

d)

(-7, -3)

61.

What is the vertex of the equation

y=(x−4)2y=\left(x-4\right)^2  

a)

(-4, 0)

b)

(4, 0)

c)

(0, 4)

d)

(0, -4)

62.

What is the vertex of the equation

y=2(x+1)2−5y=2\left(x+1\right)^2-5  

a)

(1, -5)

b)

(-1, -5)

c)

(-1, 5)

d)

(1, 5)

63.

What is the vertex of the equation

y=x2−1y=x^2-1  

a)

(0, -1)

b)

(0, 1)

c)

(1, 0)

d)

(-1, 0)

64.

What is the vertex of the equation

y=−2(x−1)2+5y=-2\left(x-1\right)^2+5  

a)

(-1, -5)

b)

(-1, 5)

c)

(1, 5)

d)

(1, -5)

65.

What direction does the following graph open?

f(x)=(x−4)2−5f\left(x\right)=\left(x-4\right)^2-5  

a)

left 

b)

right

c)

up

d)

down

66.

Does this parabola have a minimum or maximum and what is its value?

a)

minimum: 2

b)

maximum: 2

c)

minimum: 5

d)

maximum: 5

67.

Given the equation: y = -(x - 4)2 - 3,

does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

68.

What is the axis of symmetry for the equation: y = ½(x - 4)² - 4?

a)

y = 4

b)

y = - 4

c)

x = 4

d)

x = - 4

69.

What is true for: y = -2(x - 1)² + 5

a)

Opens up with a minimum

b)

Opens down with a maximum

c)

Opens left

d)

Opens right

70.

What are the x- intercepts (roots, solutions)?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

71.
Which of the following equations matches standard form of a quadratic?
a)
ax + by = c
b)
y = a(x - h)2 + k
c)
y = ax2 + bx + c
d)
y = mx + b
72.
What is the green dashed line called?
a)
roots or x-intercepts
b)
parabola
c)
axis of symmetry
d)
line of dashes
73.
If given the equation
y = 3(x + 5)2 - 4,
what is the vertex of the parabola?
a)
(5, -4)
b)
(-5, -4)
c)
(-15, -4)
d)
(15, -4)
74.

What is the vertex of the following parabola?
y=3(x+5)2−4y=3(x+5)^2-4  

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

75.

What is the vertex for the parabola?
f(x)=4(x−2)2+3f(x)=4(x-2)^2+3  

a)

(-2, 3)

b)

(2, -3)

c)

(4, 3)

d)

(2, 3)

76.

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

77.

What is true for: y = -2(x - 1)² + 5

a)

Opens up with a minimum

b)

Opens down with a maximum

c)

Opens left

d)

Opens right

78.
Does the graph of this equation open up or down? 
f(x) = -(x + 3)2 - 5
a)
up
b)
down
79.

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

80.

What does the quadratic function that has a vertex of (3,4) look like?

a)

y = a(x+3)2 + 4

b)

y = a(x-3)2 + 4

c)

y = -a(x+3) - 4

d)

y = a(x-3)2 - 4

Similar Resources on Wayground

Dec.19 Pythagorean Theorem

75 questions

Dec.19 Pythagorean Theorem

quiz

Worksheet

•

7th Grade

triangles

76 questions

triangles

quiz

Worksheet

•

1st - 12th Grade

Multiplication Fact Fluency 0-12 (Fill In Blank)

80 questions

Multiplication Fact Fluency 0-12 (Fill In Blank)

quiz

Worksheet

•

3rd - 12th Grade

Unit 1 Review

76 questions

Unit 1 Review

quiz

Worksheet

•

6th - 7th Grade

Fluency Power: #^#

75 questions

Fluency Power: #^#

quiz

Worksheet

•

7th Grade - University

Matematik Darjah 4

77 questions

Matematik Darjah 4

quiz

Worksheet

•

1st - 10th Grade

Math 7 Priority Targets

75 questions

Math 7 Priority Targets

quiz

Worksheet

•

7th Grade

bryce's 4th grade math reveiw

79 questions

bryce's 4th grade math reveiw

quiz

Worksheet

•

4th - 7th Grade