Quiz about Transformations of Quadratic Functions

Question 1

The graph of $$f\left(x\right)=x^2$$ is reflected over the x-axis and is stretched horizontally to create the graph of function $$g.$$ Which graph could represent $$g?$$

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 2

The graph of $$f\left(x\right)=x^2$$ was translated 4.5 units to the left to create the graph of function $$g.$$ Which function represents $$g?$$

Accepted Answer

$$g\left(x\right)=\left(x+4.5\right)^2$$

Answer

$$g\left(x\right)=\left(x-4.5\right)^2$$

Answer

$$g\left(x\right)=x^2-4.5$$

Answer

$$g\left(x\right)=x^2+4.5$$

Question 3

The graph of quadratic function $$f$$ was transformed to create the graph of $$g\left(x\right)=f\left(x+2\right)-5.$$ Which graph best represents $$g$$ ?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 4

The graph of $$f\left(x\right)=x^2\ $$ was transformed to create the graph of $$g\left(x\right)=f\left(x\right)-9.$$ Which statement about the graphs is true?

Accepted Answer

The y-intercept of the graph of $$g$$ is 9 units below the y-intercept of the graph of $$f.$$

Answer

The graph of $$g$$ is a reflection of the graph of $$f$$ across the x-axis.

Answer

The vertex of the graph of $$g$$ is 9 units to the right of the vertex of the graph of $$f.$$

Answer

The graph of $$g$$ is a reflection of the graph of $$f$$ across the y-axis.

Question 5

The graph of $$g\left(x\right)=x^2$$ was transformed to create the graph of $$h\left(x\right)=-\left(\frac{x}{4}\right)^2$$ . Which of these describes the transformation from the graph of $$g$$ to the graph of $$h.$$

Accepted Answer

A reflection over the x-axis and a horizontal stretch.

Answer

A reflection over the y-axis and a horizontal stretch

Answer

A reflection over the x-axis and a vertical stretch

Answer

A reflection over the y-axis an a vertical stretch

Question 6

The graph of $$f\left(x\right)=x^2\ $$ was transformed to create the graph of $$g\left(x\right)=\left(x-7.5\right)^2$$ . Which of these describes this transformation?

Accepted Answer

A horizontal shift to the right 7.5 units

Answer

A horizontal shift to the left 7.5 units

Answer

A vertical shift down 56.25 units

Answer

A vertical shift up 56.25 units

Question 7

The graph of $$g\left(x\right)=x^2$$ was transformed to create the graph of $$h\left(x\right)=3f\left(x\right)-5$$ . Which of the following statements are true?

Select TWO correct answers.

Accepted Answer

The vertex of the graph of $$h$$ is 5 units below the vertex of graph $$g$$

Answer

The graph of $$h$$ will be narrower than the graph of $$g$$

Answer

The graph of $$h$$ will be wider than the graph of $$g$$

Answer

The vertex of the graph of $$h$$ is 5 units to the right of the vetex of the graph $$g$$

Answer

The y-intercept of the graph of $$h$$ is 5 units above the vertex of graph $$g$$

Transformations of Quadratic Functions

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