Question 1

Which of the following is the correct factored form of $$x^2 - 25$?

Accepted Answer

$$(x + 5)(x - 5)$$

Question 2

What is the greatest common factor (GCF) of $$18x^3y^2$ and 24x^2$y^4$$?

Accepted Answer

$$6x^2y^2$

Question 3

A ball is thrown upward from the top of a 100-foot building with an initial velocity of 40 ft/sec. Which equation models the height $$S(t) of $$the ball after $$t$$ seconds?

Accepted Answer

$$S(t) = -16t^2$ + 40t + 100$$

Question 4

Which of the following is a correct application of the AC method for factoring $$6x^2 + 11x + 3$?

Accepted Answer

$$(2x + 3)(3x + 1)$$

Question 5

Given the quadratic function $$f(x) = -2x^2$ + 8x + 3$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, 11)$$

Question 6

Which of the following graphs best represents a function that is increasing, then constant, then decreasing?

Accepted Answer

A graph that rises, then is flat, then falls

Question 7

What is the factored form of $$x^2 + 7x + 12$?

Accepted Answer

$$(x + 3)(x + 4)$$

Question 8

If the graph of a quadratic function opens downward, which statement is true?

Accepted Answer

The leading coefficient $$a is $$negative

Question 9

Which of the following is the correct factorization of $$4x^2$$ - $$9y^2$$?

Accepted Answer

$$(2x + 3y)(2x - 3y)$$

Question 10

A student is analyzing the graph of $$y = x^2$ - 4x + 3. $$What is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 11

Which of the following best describes the range of the function $$f(x) = -x^2$ + 4$$?

Accepted Answer

$$(-\infty, 4]$$

Question 12

What is the correct interpretation of the vertex in the context of the height of a ball thrown upward?

Accepted Answer

The vertex represents the maximum height the ball reaches

Question 13

Which of the following is the correct factorization of $$x^2 - 6x + 9$?

Accepted Answer

$$(x - 3)^2$

Question 14

If $$f(x) = 2x^2$ - 8x + 6$$, what is the minimum value of the function?

Accepted Answer

$$-2$$

Question 15

Which of the following is the correct first step in factoring $$12x^3y^2$ - 8x^2$y^3$$?

Accepted Answer

Factor out $$4x^2y^2$

Question 16

A graph shows distance from home over time. If the graph is a straight line sloping upward, what does this represent?

Accepted Answer

Constant speed away from home

Factoring and Quadratic Functions: College Algebra Study Guide

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