Free Printable Quadratic Transformations (multiple)

1.

What is the vertex form of a quadratic function?

a)

f(x) = 2a(x-h)² + k

b)

f(x) = a(x-h)² + k

c)

f(x) = (x+h)² + k

d)

f(x) = a(x-h) - k

2.

Identify the vertex of f(x) = -2(x+1)² + 3

a)

(h,k)

b)

(3, 1)

c)

(-1,-3)

d)

(-1,3)

3.

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

4.

What steps transform the graph y = x² to y = 2(x+2)² - 5?

a)

Compress by 2, shifted 2 units left and 5 down

b)

Stretch by 5, shifted 5 units left and 2 down

c)

Stretch by 2, shifted 2 units left and 5 down

d)

Compress by 5, shifted 2 units left and 2 down

5.

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

a)

Compressed by 1/2, shifted 4 units right and 1 unit up

b)

Reflected across x-axis, compressed by 1/2, shifted 4 units right and 1 unit up

c)

Reflected across x-axis, stretched by 1/2, shifted 4 units left and 1 unit up

d)

Stretched by 1/2, shifted 4 units right and 1 unit down

6.

Identify the vertex of f(x) = 5(x+6)² - 7

a)

(5,6)

b)

(0,0)

c)

(6,-7)

d)

(-6,-7)

7.

Match the equation to its description.

a)

Vertically stretched by 2 and shifted up 4

b)

Vertically compressed by 2 and shifted up 4

c)

Vertically stretched by 2 and shifted left 4

d)

Vertically compressed by 2 and shifted left 4

8.

Match the equation to its description.

a)

Reflected over x-axis and shifted up 4

b)

Reflected over x-axis and shifted down 4

c)

Reflected over x-axis and shifted right 4

d)

Reflected over x-axis and shifted left 4

9.

What is the vertex of this equation?

y = (x + 4)² -6

Pay attention to negative signs!

a)

(4, 6)

b)

(-4, -6)

c)

(-4, 6)

d)

(4, -6)

10.

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)

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

11.

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)

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

12.

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)

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

13.

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)

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

14.

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

15.

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

Quadratic Transformations (multiple)

Total questions: 15

Worksheet time: 22mins

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