Free Printable Quadratics and Transformations

1.

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

2.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

3.

What is the vertex?

a)

(4,-4)

b)

(2,0)

c)

(0,2)

d)

(6,0)

4.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

5.

Write the equation of this transformation: up 8

a)

y=(x+8)²

b)

y= x²+8

c)

y= x²-8

d)

y=8x²

6.

If the blue graph is
f(x) = x²the 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

7.

Which graph has the function $f(x)=-(x+2)^2$ ?

a)

b)

c)

d)

8.

What are the solutions to this function?

a)

x={-2,-1}

b)

x={-3,-1}

c)

x={-1,3}

d)

x={-1,-2}

9.

How many solutions does this function have?

a)

two

b)

one

c)

all real numbers

d)

no real solutions

10.

What are the solutions of this graph?

a)

-2 and 3

b)

-1/2 and -6

c)

-2 and -6

d)

3 and -6

11.

.How many zeros does this parabola have?

a)

3

b)

2

c)

0

d)

1

12.

What are the x-intercepts?

a)

0 and 2

b)

-4 and 0

c)

2 and 3

d)

0 and 4

13.

Does this graph have a maximum or minimum value?

a)

maximum

b)

minimum

c)

neither

d)

both

14.

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

a)

b)

c)

d)

15.

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

16.

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

17.

How would you describe the translation from f(x)=x² to f(x)=(x-3)² ?

a)

Horizontal translation: three units to the left

b)

Horizontal translation: three units to the right

c)

Vertical translation: three units up

d)

Vertical translation: three units down

18.

What is the vertex of this quadratic equation?
y = -(x + 2)² + 4

a)

(-2,4)

b)

(2,4)

c)

(4,-2)

d)

(-4,-2)

19.

The axis of symmetry of this parabola is...

a)

y = 4

b)

y = -4

c)

x = 4

d)

x = -4

20.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

21.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

22.

Write an equation of a quadratic that is translated down 2 units.

a)

$f\left(x\right)=\left(x-2\right)^2$

b)

$f\left(x\right)=x^2-2$

c)

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

d)

$f\left(x\right)=\left(x+2\right)^2$

23.

Which equation would shift the quadratic function

f\left(x\right)=x^2

3 units left and 4 units up?

a)

$f\left(x\right)=\left(x+3\right)^2+4$

b)

$f\left(x\right)=3\left(x-4\right)^2$

c)

$f\left(x\right)=\left(x-4\right)^2+3$

d)

$f\left(x\right)=\left(x+4\right)2+3$

24.

Which equation would shift the quadratic function

f\left(x\right)=x^2

up 3 units and to the right 4 units.

a)

$f\left(x\right)=\left(x+3\right)^2+4$

b)

$f\left(x\right)=3\left(x-4\right)^2$

c)

$f\left(x\right)=\left(x-4\right)^2+3$

d)

$f\left(x\right)=\left(x+4\right)^2+3$

25.

What is the vertex?

f\left(x\right)=\left(x-4\right)^2+3

a)

(-4,3)

b)

(4,3)

c)

(-4,-3)

d)

(4,-3)

26.

What is the correct equation for this parabola?

a)

$y=\left(x-3\right)^2-1$

b)

$y=\left(x-3\right)^2+1$

c)

$y=\left(x+3\right)^2-1$

d)

$y=\left(x+3\right)^2+1$

27.

a)

F

b)

G

c)

H

d)

J

28.

a)

F

b)

G

c)

H

d)

J

29.

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

30.

Which function has a translation of 2 units right and a vertical 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

31.

Given $f\left(x\right)=\frac{1}{4}x²$ how did we transform from the parent function?

a)

Vertical compression (wider)

b)

Vertical stretch (narrower)

c)

Vertical compression (wider) and reflection over x-axis

d)

Vertical stretch (narrower) and reflection over x-axis

32.

Describe the change shown in the graph and equation. f(x) is the parent function and g(x) is the new function

f(x)= x²

g(x)= (x+2)²− 3

a)

Moved 3 to the right and 2 up

b)

Moved 2 to the left and 3 down

c)

Stretched by a factor of 3 and moved 2 to the left

d)

Compressed (shrunk) by a factor of 2 and moved 3 down

33.

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

a)

y=\left(x+3\right)^2+5

b)

$y=\left(x+5\right)^2+3$

c)

$y=\left(x-3\right)^2+5$

d)

$y=\left(x+5\right)^2-3$

34.

Find the equation of the parabola that has moved...

3 units up

a)

y=x^2+3

b)

$y=x^2-3$

c)

$y=\left(x+3\right)^2$

d)

$y=3x^2$

35.

Find the equation of the parabola that has moved...

8 units down

a)

$y=x^2+8$

b)

$y=x^2-8$

c)

$y=\left(x+8\right)^2$

d)

$y=\left(x-8\right)^2$

36.

Match the description to its equation.
Moves right 7

a)

A

b)

B

c)

C

d)

D

37.

Write the equation of this transformation: reflection across x-axis, left 3, up 15

a)

y= -(x+3)²+15

b)

y= -(x+3)² - 15

c)

y= (x+3)²+15

d)

y= -(x+15)²+3

38.

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

39.

If red represents y = x², which equation represents blue?

a)

y = 2x²

b)

y = -2x²

c)

y = -x²

d)

y = (x - 1)²

40.

If the blue graph is
f(x) = x²the 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

41.

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

42.

How did we transform from f(x) =x²

to

g(x) = -3x²

a)

reflection in x-axis and vertical shift down

b)

reflection in x-axis and vertical stretch

c)

horizontal stretch

d)

reflection in x-axis and vertical compression

43.

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

44.

Describe the transformation from dotted to solid.

a)

f(x + 5) + 3

b)

f(x +3) + 5

c)

f(x - 5) + 3

d)

f(x - 3) + 5

45.

Describe the transformation from dotted to solid.

a)

f(x + 4)

b)

f(x - 4)

c)

f(x) + 4

d)

f(x) - 4

46.

What are the transformations?
y=(x-2)³+4

a)

Horz shift right 2 Vert shift up 4

b)

Horz shift left 2 Vert shift up 4

c)

Horz shift right 2 Vert shift down 4

d)

Horz shift left 2 Vert shift up 4

47.

What causes the graph of y = x² to open downward?

a)

multiply the x² by a fraction

b)

multiply the x² by a decimal

c)

multiply the x² by a negative number

d)

multiply the x² by a number greater than 1

48.

Describe the transformation that occurred

h(x) = 1/5f(x)

a)

Up 5 Units

b)

vertical compression

c)

vertical stretch

d)

Down 5 Units

49.

Describe the transformation that occurred

k(x) = f(x) - 9

a)

vertical compression

b)

Down 9 units

c)

Left 9 units

d)

Right 9 Units

50.

Describe the transformation that occurred.

h(x) = f(x) + 2

a)

up 2 units

b)

left 2 units

c)

Vertical Strech

d)

right 2 units

51.

Describe the transformation that occurred

m(x) = f(x + 1)

a)

Left 1 Unit

b)

Right 1 unit

c)

vertical stretch

d)

up 1 unit

52.

Describe the transformation that occurred

s(x) = 7f(x)

a)

vertical compression

b)

Up 7 Units

c)

Over 7 Units

d)

vertical stretch

53.

Describe the transformation that occurred

g(x) =2f(x)

a)

Up 2 units

b)

vertical compression

c)

vertical stretch

d)

Right 2 Units

54.

Describe the transformation that occurred.

w(x) = f(x - 7)

a)

Down 7

b)

Up 7

c)

Right 7

d)

vertical compression

55.

Describe the transformation that occurred

p(x) = f(x + 3)

a)

Right 3 units

b)

Vertical Stretch

c)

Up 3 units

d)

Left 3 units

56.

How did the equation shift from the parent function? y = f(x - 4)

a)

Shift right by 4

b)

Shift left by 4

c)

Horizontal Stretch by 4

d)

Vertical Stretch by 4

e)

Shift down by 4

57.

Which transformation will occur if f(x) = x is replaced with f(x) + 2?

a)

Translation left 2 units

b)

Translation right 2 units

c)

Vertical translation up by 2 units.

d)

Reflection across the x-axis.

58.

What is the slope in the picture?

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

59.

What is the slope in the picture?

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

60.

What type of slope does the following graph have?

a)

Postive

b)

Negative

c)

Zero Slope

d)

Undefined

Quadratics and Transformations

Total questions: 60

Worksheet time: 2hrs 40mins

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