Free Printable Quadratic Transformations

1.

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)

2.

Which equation would shift the following quadratic up 3 units?

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

a)

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

b)

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

c)

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

d)

$f\left(x\right)=\left(x-7\right)^2$

3.

What is the vertex?

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

a)

(-2,5)

b)

(2,5)

c)

(2,-5)

d)

(-2,-5)

4.

Which equation would shift the quadratic equation right 3?

f\left(x\right)=2\left(x+1\right)^2+6

a)

$f\left(x\right)=2\left(x-3\right)^2+6$

b)

$f\left(x\right)=2\left(x-2\right)^2+6$

c)

$f\left(x\right)=2\left(x+1\right)^2+9$

d)

$f\left(x\right)=2\left(x+4\right)^2+6$

5.

What is the new equation of the quadratic below that has a vertical shift of 4 units?

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

a)

$f\left(x\right)=-\left(x+6\right)^2-5$

b)

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

c)

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

d)

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

6.

What is the vertex?

f\left(x\right)=2\left(x+1\right)^2+6

a)

(-1, 6)

b)

(2, 1)

c)

(1, 6)

d)

(6, -1)

7.

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)

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

8.

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)

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

9.

Which equation would vertically stretch the quadratic function

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

by a factor of 3 and shift it 4 to the right?

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)

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

10.

Which quadratic function below is not reflected down?

a)

$f\left(x\right)=-\frac{1}{2}\left(x+3\right)^2+4$

b)

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

c)

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

d)

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

11.

Describe the transformation:

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

a)

right 3, down 2

b)

up 3, left 2

c)

left 3, up 2

d)

left 3, down 2

12.

Describe the transformation:

f\left(x\right)=\frac{1}{2}x^2+4

a)

right 1/2 and up 4

b)

Vertical Compression of 1/2 and up 4

c)

Vertical Stretch of 1/2 and up 4

d)

Vertical Compression of 1/2 and down 4

13.

Describe the transformation:

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

a)

right 3

b)

Reflected down, right 3

c)

Reflected down, up 3

d)

Reflected down, left 3

14.

What is the vertex?

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

a)

(3,0)

b)

(-3,0)

c)

(0,3)

d)

(0,-3)

15.

Which equation matches the following transformation: up 4, stretched 3, reflected down, and left 1

a)

$f\left(x\right)=-3\left(x+1\right)^2+4$

b)

$f\left(x\right)=-4\left(x+3\right)^2+1$

c)

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

d)

$f\left(x\right)=3\left(x+1\right)^2+4$

16.

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)

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

17.

Which quadratic would be the narrowest?

a)

$f\left(x\right)=\frac{1}{2}x^2$

b)

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

c)

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

d)

$f\left(x\right)=5x^2$

18.

Describe the transformation:

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

a)

left 4, up 2

b)

reflected down, right 4, up 2

c)

reflected down, left 4, up 2

d)

reflected down, up 4, right 2

19.

A quadratic is reflected down when the value of a is negative.

a)

TRUE

b)

FALSE

20.

What shape is the graph of a parabola?

a)

Line

b)

V-Shaped

c)

Parabola

d)

Happy Face

Quadratic Transformations

Total questions: 20

Worksheet time: 10mins

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