Question 1

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

Accepted Answer

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

Question 2

Which letter on the graph corresponds to the vertex of the parabola?

Accepted Answer

c

Question 3

Given the quadratic $$y = -3(x - 2)^2$ + 4$$, does the function have a minimum or maximum value?

Accepted Answer

Maximum

Question 4

Rewrite $$f(x) = x^2$ - 12x + 32 in $$vertex form and state the vertex.

Accepted Answer

$$f(x) = (x - 6)^2$ - 4$$, vertex: $$(6, -4)$$

Question 5

What are the solutions (roots/zeroes) of $$f(x) = x^2$ - 5x - 6$$?

Accepted Answer

$$x = 6$$ and $$x = -1$$

Question 6

A baseball player throws a rock upward from a 112-foot cliff at 96 ft/s. The height is modeled by $$f(t) = -16t^2$ + 96t + 112. $$When does the rock reach its maximum height?

Accepted Answer

$$t = 3$$ seconds

Question 7

For the function $$g(x) = x^2$ + 4x + 5$$, what are the solutions (roots/zeroes)?

Accepted Answer

$$x = -2 \pm i$$

Question 8

You are building a rectangular fence with 200 feet of fencing. What dimensions maximize the area?

Accepted Answer

$$L = 50 ft$$, $$W = 50 ft$$

Question 9

Which letter on the graph corresponds to the axis of symmetry?

Accepted Answer

d

Question 10

Given $$h(x) = x^2$ - 2x$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 11

Which of the following is the general form of a quadratic equation?

Accepted Answer

$$y = ax^2$ + bx + c$$

Question 12

For the function $$y = 2x^2$ - 6x + 5$$, does the parabola have a minimum or maximum?

Accepted Answer

Minimum

Question 13

If the axis of symmetry of a parabola is $$x = 4$$, what is the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = 4$$

Question 14

Given $$g(x) = 2x^2$ + 8x - 10$$, rewrite in vertex form and state the vertex.

Accepted Answer

$$g(x) = 2(x + 2)^2$ - 18$$, vertex: $$(-2, -18)$$

Question 15

A rock is thrown from a cliff and its height is modeled by $$f(t) = -16t^2$ + 96t + 112. $$What is the maximum height reached by the rock?

Accepted Answer

$$256$$ feet

Question 16

For the function $$y = -x^2$ + 7x$$, does the parabola have a minimum or maximum?

Accepted Answer

Maximum

Question 17

Which letter on the graph corresponds to the $$y-$$intercept?

Accepted Answer

b

Question 18

If the domain of a quadratic function is all real numbers, what is the range of $$y = (x - 1)^2$ - 2$$?

Accepted Answer

$$y \geq -2$$

Question 19

If a quadratic function opens upward, what can you say about the leading coefficient $$a$$?

Accepted Answer

$$a \u003e 0$$

Question 20

A rectangular garden is to be fenced with 200 feet of fencing. What is the maximum area that can be enclosed?

Accepted Answer

$$2500 ft$^2$$

Quadratic Functions and Their Properties – Precalculus Study Guide

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