Quiz about Quadratic Transformations Practice

Question 1

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

Accepted Answer

- Vertical stretch of 3

- Shift up 5 units

Answer

- Horizontal stretch of 3

- Shift down 5 units

Answer

-Reflection over x-axis

-Vertical shrink of 3

-Shift up 5 units

Answer

- It is exactly the same

Question 2

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

Accepted Answer

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

- shift down 2 units

Answer

- vertical shrink of 2

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

Answer

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

- shift down 2 units

Answer

- reflection over

y-axis

- shift down 2 units

Question 3

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

Accepted Answer

- Horizontal shrink of 9

- Shift right 3 units

- Shift down 1 unit

Answer

- Horizontal stretch of 3

- Shift right 3 units

- Shift down 1 unit

Answer

- Vertical stretch of 3

- Shift right 3 units

- Shift down 1 unit

Answer

- Vertical shrink of 9

- Shift left 3 units

- Shift up 1 unit

Question 4

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

Accepted Answer

- reflection over

x - axis

- vertical stretch of 2

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

- shift left 7 units

Answer

- reflection over

y - axis

- vertical stretch of 2

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

- shift left 7 units

Answer

- reflection over

x - axis

- vertical shrink of 2

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

- shift right 7 units

Answer

- reflection over

y - axis

- vertical shrink of 2

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

- shift right 7 units

Question 5

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

Accepted Answer

- reflection over

x-axis

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

- shift left 1 unit

- shift up 5 units

Answer

- shift left 1 unit

- shift up 5 unit

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

-reflection over x-axis

Answer

- reflection over

y-axis

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

- shift left 1 unit

- shift up 5 units

Answer

- reflection over

y-axis

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

- shift left 1 unit

- shift up 5 units

Question 6

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

Accepted Answer

- reflection over

y - axis

- horizontal shrink of 3/2

- shift left 4 units

- shift down 5 units

Answer

- reflection over

x - axis

- vertical stretch of 3/2

- shift left 4 units

- shift down 5 units

Answer

- reflection over

y - axis

- vertical stretch of 3/2

- shift right 4 units

- shift down 5 units

Answer

- reflection over

x - axis

- horizontal stretch of 3/2

- shift right 4 units

- shift down 5 units

Question 7

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

Accepted Answer

- reflection over

x-axis

- shift up 1 unit

Answer

- reflection over

x-axis

- shift down 1 unit

Answer

- reflection over

y-axis

- shift down 1 unit

Answer

- reflection over

x-axis

- shift right 1 unit

Question 8

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

Accepted Answer

- reflection over

x-axis

- vertical shrink of 1/3

- shift left 8 units

- shift down 3 units

Answer

- reflection over

y-axis

- vertical stretch of - 1/3

- shift left 8 units

- shift down 3 units

Answer

- reflection over

x-axis

- vertical shrink of 1/3

- shift right 8 units

- shift down 3 units

Answer

- reflection over

y-axis

- vertical stretch of 1/3

- shift left 8 units

- shift down 3 units

Question 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?

Accepted Answer

$$5x^2+13$$

Answer

Answer

$$-5x^2-7$$

Answer

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

Question 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?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Quadratic Transformations Practice

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