Free Printable Quadratic Transformations Practice

1.

Describe how the following quadratic equation $f\left(x\right)=3x^2+5$ compares to the parent function $f\left(x\right)\ =\ x^2$

a)

- Vertical stretch of 3

- Shift up 5 units

b)

- Horizontal stretch of 3

- Shift down 5 units

c)

-Reflection over x-axis

-Vertical shrink of 3

-Shift up 5 units

d)

- It is exactly the same

2.

Describe how the quadratic function $f\left(x\right)=\ \frac{6}{7}x^2-2$ compares to the parent function $f\left(x\right)\ =\ x^2$

a)

- vertical shrink of 2

- shift up $\frac{6}{7}$ units

b)

- horizontal shrink of $\frac{6}{7}$

- shift down 2 units

c)

- vertical shrink of $\frac{6}{7}$

- shift down 2 units

d)

- reflection over

y-axis

- shift down 2 units

3.

Describe how the quadratic function $f\left(x\right)\ =\ \left(9x-3\right)^2-1$ compares to the parent function

a)

- Horizontal shrink of 9

- Shift right 3 units

- Shift down 1 unit

b)

- Horizontal stretch of 3

- Shift right 3 units

- Shift down 1 unit

c)

- Vertical stretch of 3

- Shift right 3 units

- Shift down 1 unit

d)

- Vertical shrink of 9

- Shift left 3 units

- Shift up 1 unit

4.

Describe how the quadratic function $f\left(x\right)\ -2\left(\frac{1}{4}x+7\right)^2$ compares to the parent function.

a)

- reflection over

x - axis

- vertical stretch of 2

- horizontal stretch of $\frac{1}{4}$

- shift left 7 units

b)

- reflection over

y - axis

- vertical stretch of 2

horizontal shrink of $\frac{1}{4}$

- shift left 7 units

c)

- reflection over

x - axis

- vertical shrink of 2

- horizontal stretch of $\frac{1}{4}$

- shift right 7 units

d)

- reflection over

y - axis

- vertical shrink of 2

horizontal stretch of $\frac{1}{4}$

- shift right 7 units

5.

Describe the quadratic transformations of the following equation $f\left(x\right)=-\frac{2}{3}\left(x+1\right)^2+5$

a)

- shift left 1 unit

- shift up 5 unit

- horizontal shrink of $\frac{2}{3}$

-reflection over x-axis

b)

- reflection over

y-axis

- vertical stretch of $-\frac{2}{3}$

- shift left 1 unit

- shift up 5 units

c)

- reflection over

x-axis

- vertical shrink of $\frac{2}{3}$

- shift left 1 unit

- shift up 5 units

d)

- reflection over

y-axis

- horizontal shrink of $\frac{2}{3}$

- shift left 1 unit

- shift up 5 units

6.

Describe the quadratic transformations of the following equation $f\left(x\right)\ =\ \left(-\frac{3}{2}x+4\right)^2-5$

a)

- reflection over

x - axis

- vertical stretch of 3/2

- shift left 4 units

- shift down 5 units

b)

- reflection over

y - axis

- vertical stretch of 3/2

- shift right 4 units

- shift down 5 units

c)

- reflection over

x - axis

- horizontal stretch of 3/2

- shift right 4 units

- shift down 5 units

d)

- reflection over

y - axis

- horizontal shrink of 3/2

- shift left 4 units

- shift down 5 units

7.

Describe the quadratic transformations of the following equation $f\left(x\right)\ =\ -x^2+1$

a)

- reflection over

x-axis

- shift up 1 unit

b)

- reflection over

x-axis

- shift down 1 unit

c)

- reflection over

y-axis

- shift down 1 unit

d)

- reflection over

x-axis

- shift right 1 unit

8.

Describe the quadratic transformations of the following equation $f\left(x\right)\ =\ -\frac{1}{3}\left(x+8\right)^2-3$

a)

- reflection over

x-axis

- vertical shrink of 1/3

- shift left 8 units

- shift down 3 units

b)

- reflection over

y-axis

- vertical stretch of - 1/3

- shift left 8 units

- shift down 3 units

c)

- reflection over

x-axis

- vertical shrink of 1/3

- shift right 8 units

- shift down 3 units

d)

- reflection over

y-axis

- vertical stretch of 1/3

- shift left 8 units

- shift down 3 units

9.

Given the function $f\left(x\right)\ =\ 5x^2+3$ , what would the new equation be if the transformation $f\left(x\right)+10$ was plotted?

a)

$5x^2-7$

b)

$-5x^2-7$

c)

$5x^2+13$

d)

$\frac{50}{3}x^2+10$

10.

Given the function $f\left(x\right)=\ 3\left(x-2\right)^2-4$ , what would the new equation be if $f\left(x\right)$ was reflected over the y-axis, translated 8 units left and 10 units up?

a)

$-3\left(x-10\right)^2+6$

b)

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

c)

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

d)

$3\left(-x+8\right)^2+10$

Quadratic Transformations Practice

Total questions: 10

Worksheet time: 3hrs 30mins

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