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Quadratic Transformation Practice

Total questions: 79

Worksheet time: 7hrs 42mins

Name
Class
Date
1.

What is the parent function of a quadratic?

a)

y=xy=x

b)

y=x2y=x^2

c)

y=xy=\sqrt{x}

d)

y=∣x∣y=\left|x\right|

2.

Which transformation transforms the graph of

f(x) = x2 to the graph of g(x) = (x + 4)2?

a)

shift 4 units up

b)

shift 4 units down

c)

shift 4 units to the left

d)

shift 4 units to the right

3.

How did we transform from y=x2 to

y = -3x2

a)

reflection in x-axis and shifts down

b)

reflection x-axis and narrower

c)

wider

d)

reflection x-axis and wider

4.
If the blue graph 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
5.
Does the graph of this equation widen or narrow from the parent function?
y=  5(x - 5)2 + 3
a)
widen
b)
narrow
c)
neither
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.
If red represents y = x2, which equation represents blue?
a)
y = 2x2
b)
y = -2x2
c)
y = -x2
d)
y = (x - 1)2
8.

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)

9.

What are the transformations?

y=(x-2)2+4 (Choose ALL that apply.)

a)

shift right 2

b)

shift left 2

c)

shift up 4

d)

shift down 4

10.

Write 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

11.

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

12.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 1

b)

y = - x2

c)

y = ( - x - 1 )2

d)

y = ( - x + 1 )2

13.

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

14.

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

15.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 4

b)

y = x2 + 4

c)

y = ( x - 4 )2

d)

y = ( x + 4 )2

16.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 3

b)

y = x2 + 3

c)

y = ( x - 3 )2

d)

y = ( x + 3 )2

17.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 2

b)

y = x2 + 2

c)

y = ( x - 2 )2

d)

y = ( x + 2 )2

18.

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

19.

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

20.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 2

b)

y = x2 + 2

c)

y = ( x - 2 )2

d)

y = ( x + 2 )2

21.

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

22.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 3

b)

y = x2 + 3

c)

y = ( x - 3 )2

d)

y = ( x + 3 )2

23.

Write the equation of the quadratic function. (parabola)

a)

y = x2 - 7

b)

y = x2 + 7

c)

y = ( x - 7 )2

d)

y = ( x + 7 )2

24.

Write 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

25.
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
26.
How did we transform from the parent function?
g(x) = -1/5(x - 1)2 + 7
a)

reflection, compression, horizontal right, vertical shift up

b)

compression, horizontal shift left, vertical shift up

c)
reflection, horizontal shift right, vertical shift down
d)
no changes were made to y = x2
27.
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
28.
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
29.
Does the graph of this equation open up or down? 
f(x) = -(x + 3)2 - 5
a)
up
b)
down
30.
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
31.

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

a)

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

b)

Compress by a factor 2 and vertical shift up 4

c)

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

d)

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

32.
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
33.

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

34.
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
35.
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
36.

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)?

 (Blue is f(x) and red is g(x) )

a)

g(x) = 2x2g\left(x\right)\ =\ 2x^2

b)

g(x) = 0.5x2g\left(x\right)\ =\ 0.5x^2

c)

g(x) = x2 + 2g\left(x\right)\ =\ x^2\ +\ 2

d)

g(x) = (x+2)2g\left(x\right)\ =\ \left(x+2\right)^2

37.

Match the equation to its description.

a)

Reflected , right 2 and up 1

b)

Reflected , left 2 and up 1

c)

Reflected , right 2 and down 1

d)

Reflected , left 2 and down 1

38.
Which of the following is the correct equation for the given graph?
a)
f(x) = (x - 2)2 - 1
b)
f(x) = (x + 2)2 - 1
c)
f(x) = -(x + 2)2 - 1
d)
f(x) = -(x - 2)2 - 1
39.
Name the parent function.
a)
linear
b)
quadratic
c)
cubic
d)
logarithmic
40.

What is the axis of symmetry?

a)

A line whose equation is the x-coordinate of a parabola's vertex

b)

A central line that divides a parabola into mirror images

c)

A line that intersects a parabola at the vertex

d)

All of the above

41.

Which of the following graphs appropriately marks the axis of symmetry?

a)
b)
c)
d)
42.
Does this graph have a maximum or minimum value?
a)
maximum
b)
minimum
c)
neither
d)
both
43.

Using the graph of the quadratic function, identify the vertex.

a)

(4, -6)

b)

(0, 2)

c)

(.5, 0)

d)

(7.5, 0)

44.
What are the x-intercepts?
a)
0 and 2
b)
-4 and 0
c)
2 and 3
d)
0 and 4
45.

Using the graph of the quadratic function, identify the y-intercept.

a)

(4, -6)

b)

(0, 2)

c)

(.5, 0)

d)

(7.5, 0)

46.
Which function has a translation of 3 units to the left?
a)
f(x) = 3x2+1
b)
f(x) = (x + 3)2 + 1
c)
f(x) = (x - 3)2 + 1
d)
f(x) = (x + 1)2- 3
47.

Which function has a translation of 2 units right and a stretch by a factor of 5?

a)
f(x)= 5(x - 2)2
b)
f(x) = 5(x + 2)2
c)
f(x) = (x - 2)2 - 5
d)
f(x) = (x + 2)2 + 5
48.
Which function has a translation of 7 units down and reflects over the x-axis?
a)
f(x) = -(x - 7)2 + 1
b)
f(x) = (x + 7)2 + 1
c)
f(x) = -(x - 1)2 - 7
d)
f(x) = (x + 1)2 - 7
49.
What describes the effect on the graph of the equation y = 3x2 when it is changed to y = -¾x2?
a)
The graph is congruent and is translated down.
b)
The graph is wider and opens downward.
c)
The graph is congruent and is translated up.
d)
The graph is narrower and opens downward.
50.
Which quadratic is the narrowest graph?
a)
y = 3x2
b)
y = 4x2
c)
y = 2x2
51.
Which quadratic is wider than the graph of y = 4x2 + 5?
a)

y = 6x2 + 5

b)
y = 5x2 + 5
c)
y = 0.25x2 + 5
d)

y = 4x2+5

52.

What is the orange line called?

a)

Line of Solutions

b)

Roots

c)

Vertex

d)

Axis of Symmetry

53.

The graph of a quadratic function is called a

a)

line

b)

parabola

c)

half oval

d)

vertex form

54.

If the vertex of this graph is (2, -1), what is the axis of symmetry?

a)

x= -1

b)

x = 2

c)

y = -1

d)

x = -2

55.
What are the x- intercepts?
a)
x= 0 and x= -4
b)
x= 0 and x= 4
c)
y= 0
d)
x= 2
56.
The axis of symmetry line passes through which point?
a)
y-intercept
b)
any random point
c)
vertex
d)
symmetrical point for the vertex
57.
Does the quadratic have a max/min vertex, and does the parabola open up/down?
a)
max/ opens down
b)
min/ opens up
c)
max/ opens up
d)
min/ opens down
58.
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
59.
Which equation has a vertex of (-3, 4)?
a)
y = 2(x+3)2 + 4
b)
y = (x+3)2 - 4
c)
y = (x-3)2 + 4
d)
y = 2(x - 3)2 + 4
60.

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)

61.
What is the vertex of the parabola: y=2(x-3)2+4
a)
(3,4)
b)
(-3,4)
c)
(3, -4)
d)
(-3,-4)
62.
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
63.
What is the vertex of y = 2(x - 3)2 + 6
a)
(-3, -6)
b)
(3, -6)
c)
(-3, 6)
d)
(3, 6)
64.

What is the green dot on the parabola called?

a)

maximum

b)

minumum

c)

roots

d)

zeros

65.

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

66.

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

does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

67.

What is the equation of this graph?

a)

f(x) = (x -5)2 + 1

b)

f(x) = (x - 1)2 - 5

c)

f(x) = (x + 1)2 - 5

d)

f(x) = (x + 5)2 +1

68.
Does the graph of this equation open up or down? 
f(x) = -(x + 3)2 - 5
a)
up
b)
down
69.
What is the equation for axis of symmetry?
a)
y=3
b)
x=3
c)
x=5
d)
x=1
70.

What are the green points called?

a)
axis of symmetry
b)
vertex
c)

y-intercept

d)

x-intercepts

71.
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)
72.
What is the vertex?
f(x) = 2(x - 5)2 + 12
a)
(-5, -12)
b)
(5,-12)
c)
(5, 12)
d)
(-5, 12)
73.
In vertex form, what effect does the h have on the graph?
a)
Translates Up/Down
b)
Translates Left/Right
c)
Narrows/Widens Parabola
d)
Flips it
74.
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
75.
Shift f(x)=x2 three units to the left and 4 units down
a)
f(x)=(x+3)2-4
b)
f(x)=(x-3)2-4
c)
f(x)=(x+4)2-3
d)
f(x)=(x-4)2-3
76.
How would you describe the translation from f(x)=x2  to  f(x)=x2+5 ?
a)
Horizontal translation: five units to the right
b)
Horizontal translation: five units to the left
c)
Vertical translation: five units up
d)
Vertical translation: five units down
77.
a)
y=(x-2)2+3
b)
y=(x-2)2-3
c)
y=(x+2)2+3
d)
y=(x+2)2-3
78.
a)
y=(x-4)2+1
b)
y=(x-4)2-1
c)
y=(x+4)2+1
d)
y=(x+4)2-1
79.
What is the vertex?
a)
(2, 4)
b)
(3, -1)
c)
(0, 8)
d)
(4, 2)

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