Question 1

Given the graph of the quadratic function in the first image, which of the following is the correct factored form of the function?

Accepted Answer

$$f(x) = (x + 3)(x - 4)$$ with a leading coefficient$$, f(x) = a(x + 3)(x - 4)$$,	ext{ where } a = 1$

Question 2

For the quadratic function in the second image, what is the vertex of the parabola?

Accepted Answer

$$(3.5, 13.25)$$

Question 3

Which of the following equations best represents the function in the third image?

Accepted Answer

$$f(x) = x^2$ - 2x - 3$$

Question 4

Which parent function is shown in the fourth image?

Accepted Answer

$$f(x) = x^2$

Question 5

The graph in the fifth image is an example of which type of power function?

Accepted Answer

$$f(x) = x^3$

Question 6

Using the table in the sixth image, what is the best power function model for the braking distance $$d (in $$feet) as a function of speed $$s (in $$mph)?

Accepted Answer

$$d = 0.05s^2$

Question 7

For the function shown in the seventh image, what is the domain?

Accepted Answer

$$[0, 1]$$

Question 8

In the eighth image, what transformation does $$y = f(x) + c$$ represent?

Accepted Answer

A vertical shift upward by $$c$$ units

Question 9

In the ninth image, what transformation is shown between $$y = f(x)$$ and $$y = -f(x)$$?

Accepted Answer

Reflection over the $$x-$$axis

Question 10

Suppose a quadratic function models the height $$h(t) of a $$ball thrown upward as $$h(t) = -16t^2$ + 80t + 96. $$What is the initial height of the ball?

Accepted Answer

$$96$$ feet

Question 11

Given the quadratic function $$f(x) = ax^2$ + bx + c$$, if $$a \u003c 0$$, what can you say about the graph?

Accepted Answer

It opens downward

Question 12

If the discriminant $$D = b^2$ - 4ac of a $$quadratic equation is negative, what does this indicate about the solutions?

Accepted Answer

There are no real solutions

Question 13

Which of the following is the vertex form of a quadratic function?

Accepted Answer

$$f(x) = a(x - h)^2$ + k$$

Question 14

If $$f(x) = x^2$ - 2x - 3$$, what are the zeros of the function?

Accepted Answer

$$x = -3$$ and $$x = 1$$

Question 15

Given the function $$f(x) = \sqrt{x}$$, what is the range?

Accepted Answer

$$[0, \infty)$$

Question 16

If $$f(x) = x^2$ and g(x) = x + 1$, what is the composition f(g(x$$))$$?

Accepted Answer

$$(x + 1)^2$

Question 17

Which of the following describes the effect of multiplying a function $$f(x) by a $$constant $$a \u003e 1$$?

Accepted Answer

Vertical stretch

Question 18

If $$f(x) = x^2$ and g(x) = -f(x$$)$$, what transformation has occurred?

Accepted Answer

Reflection over the $$x-$$axis

Question 19

Given the function $$f(x) = \frac{1}{x - 2}$$, what is the domain?

Accepted Answer

$$x 
eq 2$$

Question 20

If $$f(x) = x^2$ - 4x + 3$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 2$$

Comprehensive Study Notes: Quadratic and Power Functions, Domain & Range, Function Transformations

Study Guide - Practice Questions

Study Guide - Flashcards