$$6 + 4[3 \times 36 \div 12] = 6 + 4[108 \div 12] = 6 + 4[9] = 6 + 36 = 42$$

$$t = \frac{-b}{2a} = \frac{-200}{2 \times -16} = 6.25$$ seconds

Question 1

Which of the following correctly applies the order of operations to evaluate $$6 + 4[3(6^2$) \div 12]$$?

Accepted Answer

$$6 + 4[3 	imes 36 \div 12] = 6 + 4[108 \div 12] = 6 + 4[9] = 6 + 36 = 42$$

Question 2

What is the result of $$(-3)^2$$ and $$-3^2$$?

Accepted Answer

$$(-3)^2 = 9$ and -3^2$ = -9$$

Question 3

Which property of exponents is used to simplify $$(a^m)^n$$?

Accepted Answer

Power of a Power Property: $$(a^m)^n = a$$^{mn}$$

Question 4

Which of the following is the correct factorization of $$49x^2 - 126xy$$ + $$81y^2$$?

Accepted Answer

$$(7x - 9y)^2$

Question 5

Given the quadratic function $$y = 3x^2$ - 12x + 8$$, what is the axis of symmetry?

Accepted Answer

$$x = \frac{-b}{2a} = \frac{12}{6} = 2$$

Question 6

Which interval notation represents the solution to $$x \u003c 2 or$$ $$x \geq 8$$?

Accepted Answer

$$(-\infty, 2) \cup [8, \infty)$$

Question 7

A model rocket is launched upward with $$h(t) = -16t^2$ + 200t. $$When does it reach its maximum height?

Accepted Answer

$$t = \frac{-b}{2a} = \frac{-200}{2 	imes -16} = 6.25$$ seconds

Question 8

Which of the following is the correct vertex form for $$y = x^2$ + 16x - 33$$?

Accepted Answer

$$y = (x + 8)^2$ - 97$$

Question 9

Which set notation correctly represents all $$x$$ such that $$x is $$less than or equal to 2?

Accepted Answer

$$\{x \mid x \leq 2\}$$

Question 10

Which of the following is a perfect square trinomial?

Accepted Answer

$$x^2 + 12x + 36$

Question 11

If a quadratic function opens downward, which statement is true about its leading coefficient?

Accepted Answer

The leading coefficient $$a is $$less than zero ($$a \u003c 0)$$

Question 12

Which of the following is the correct domain in interval notation for the function $$f(x) = x^2$?

Accepted Answer

$$(-\infty, \infty)$$

Question 13

What is the solution to the equation $$\frac{x+3}{4} = \frac{x+6}{6}$$?

Accepted Answer

$$x = 3$$

Question 14

Which of the following is the correct interval notation for $$2 \u003c x \leq 6$$?

Accepted Answer

$$(2, 6]$$

Question 15

Which property of exponents is used to simplify $$\frac{a^m}{a^n}$$?

Accepted Answer

Quotient Property: $$\frac{a^m}{a^n} = a$$^{m-n}$$

Question 16

Which of the following is the correct factorization for $$x^2 - 49$?

Accepted Answer

$$(x - 7)(x + 7)$$

Question 17

Which of the following is the correct solution for the equation $$7x + 3(x - 4) = 6 + 2(x + 11)$$?

Accepted Answer

$$x = 5$$

Question 18

Which of the following is the correct domain in set notation for the function $$y = 3x - 2$$?

Accepted Answer

$$\{x \mid x \in \mathbb{R}\}$$

Algebraic Foundations and Quadratic Functions: Precalculus Study Guide

Study Guide - Practice Questions