Quiz about Representing and Comparing Transformations

Question 1

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

Accepted Answer

vertical shift up 5 units

Answer

horizontal shift right 5 units

Answer

horizontal shift left 5 units

Answer

vertical shift down 5 units

Question 2

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

Accepted Answer

horizontal shift left 7 units

Answer

horizontal shift right 7 units

Answer

vertical shift up 7 units

Answer

vertical shift down 7 units

Question 3

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

Accepted Answer

Vertical stretch by a factor of 5

Answer

Vertical shrink/compress by a factor of 5

Answer

Reflect over x-axis

Answer

Vertical shift up 5 units

Question 4

Which of the following describes the transformations done to the quadratic parent function of f(x) = x² to obtain g(x) = 2x² + 4 ?

Accepted Answer

Vertical Stretch by a factor of 2 and vertical shift up 4 units

Answer

Vertical Shrink/Compress by a factor 2 and vertical shift up 4

Answer

Vertical Stretch by a factor of 2 and horizontal shift left 4 units

Answer

Vertical Shrink/Compress by a factor of 2 and horizontal shift right 4 units

Question 5

If the blue is f(x)=x^2,the red must be

Accepted Answer

g(x)=(x-3)²

Answer

g(x)=(x+3)²

Answer

g(x)=x2+3

Answer

g(x)=x2-2

Question 6

Which of the following is the correct equation for the given graph?

Accepted Answer

f(x) = (x + 2)² - 1

Answer

f(x) = (x - 2)² - 1

Answer

f(x) = -(x + 2)² - 1

Answer

f(x) = -(x - 2)² - 1

Question 7

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

Accepted Answer

(-5, -4)

Answer

(5, -4)

Answer

(-15, -4)

Answer

(15, -4)

Question 8

Does the graph of this equation open up or down?

f(x) = -(x + 3)² - 5

Accepted Answer

down

Answer

up

Question 9

What equation represents the quadratic function?

Accepted Answer

y = -x² + 5

Answer

y = -(x - 5)²

Answer

y = x² - 5

Answer

y = (x - 5)²

Question 10

y=2x²-6x+1 is in what form?

Accepted Answer

Standard Form

Answer

Vertex Form

Answer

Factored form

Answer

Cannot be determined

Question 11

The graph of g(x) = x² is transformed to create the graph of g(x) = -g(x). Describe the transformation.

Accepted Answer

Reflection in the x-axis.

Answer

Vertical shift up.

Answer

Horizontal shift to the right.

Answer

Horizontal shift to the left.

Question 12

The graph of m(x) = x² was transformed to create the graph of n(x) = x² + 21. Which of these describes the transformation?

Accepted Answer

A vertical shift up 21 units.

Answer

A vertical shift down 21 units.

Answer

A horizontal shift to the right 21 units.

Answer

A horizontal shift to the left 21 units.

Question 13

The graph of g(x) = x² is transformed to create the graph of h(x) = 0.5g(x). Describe the transformation.

Accepted Answer

Vertical shrink/compression by a factor of 0.5

Answer

Vertical stretch by a factor of 0.5.

Answer

Horizontal stretch by a factor of 0.5.

Answer

Horizontal shrink/compression by a factor of 0.5.

Question 14

Quadratic function f(x)=x² is graphed on a coordinate plane. The graph of a new quadratic is formed by changing the vertex to (3, 0). Which function could represent the new quadratic?

Accepted Answer

g(x) = (x - 3)²

Answer

g(x) = x²- 3

Answer

g(x) = x²+ 3

Answer

g(x) = (x + 3)²

Question 15

Which two transformations can be used to obtain the graph of h(x)= -x²- d from the function f(x) = x²?

Accepted Answer

A reflection across the x-axis followed by a translation down d units.

Answer

A reflection across the x-axis followed by a translation up d units.

Answer

A reflection across the y-axis followed by a translation to the right d units.

Answer

A reflection across the y-axis followed by a translation to the left d units.

Question 16

What is the equation of the parabola shown?

Accepted Answer

g(x) = - (x + 1)²

Answer

g(x) = - (x - 1)²

Answer

g(x) = (x - 1)²

Answer

g(x) = - x² + 1

Question 17

Describe the transformation of y = (x - 4)²

Accepted Answer

Shift RIGHT

Answer

Shift UP

Answer

Shift DOWN

Answer

Shift LEFT

Question 18

Describe the transformation of y = x² + 4

Accepted Answer

Shift UP

Answer

Shift DOWN

Answer

Shift LEFT

Answer

Shift RIGHT

Question 19

How did we transform from the parent function?
y = x² + 2

Accepted Answer

vertical shift up

Answer

horizontal shift up

Answer

horizontal shift down

Answer

vertical shift down

Question 20

Match the equation to its description.

Accepted Answer

Reflected over x and stretched by 3

Answer

Stretched by 3

Answer

Reflected over x

Answer

Reflected over x and up 3

Question 21

Match the equation to its description.

Accepted Answer

Right 2 and up 2

Answer

Left 2 and up 2

Answer

Right 2 and down 2

Answer

Left 2 and down 2

Question 22

Match the equation to its description.

Accepted Answer

Reflected over x, right 2 and up 1

Answer

Reflected over x, left 2 and up 1

Answer

Reflected over x, right 2 and down 1

Answer

Reflected over x, left 2 and down 1

Question 23

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

Accepted Answer

y = -7x2

Answer

y = 7x2

Answer

y = -(1/7)x²

Answer

y = -5x2

Question 24

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

Accepted Answer

horizontal shift left 7 units

Answer

horizontal shift right 7 units

Answer

vertical shift up 7 units

Answer

vertical shift down 7 units

Question 25

What is the equation of the quadratic function obtained from vertically compressing the parent function by 3/5 and then shifted up 8 units?

Accepted Answer

f(x)=3/5x²+8

Answer

f(x)= 3/5(x-8)²

Answer

f(x)=x2

Answer

f(x)=3/5x²-8

Representing and Comparing Transformations

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