Question 1

Find the zeros of the function $$f(x) = 6x^2$ + 13x - 5. $$Which of the following lists all zeros as ordered pairs?

Accepted Answer

Question 2

Which of the following is the correct solution set in interval notation for the inequality $$x^2 - 2x - 24$$ \geq 0$$?

Accepted Answer

$$(-\infty, -6] \cup [4, \infty)$$

Question 3

Solve the absolute value equation $$|3x - 1| = 2. $$What is the solution set?

Accepted Answer

$$\left\{1, -\frac{1}{3}\right\}$$

Question 4

Given the quadratic function $$f(x) = -3x^2$ + 6x + 1$$, which of the following statements is true?

Accepted Answer

The function is concave down and has a maximum at its vertex.

Question 5

What is the equation of the axis of symmetry for the function $$f(x) = -3x^2$ + 6x + 1$$?

Accepted Answer

$$x = 1$$

Question 6

A company’s demand equation is $$x = -6p + 600$$, where $$x is $$the quantity sold and $$p is $$the price in dollars. Which of the following expresses the revenue $$R as a $$function of $$p$$?

Accepted Answer

$$R(p) = -6p^2$ + 600p$$

Question 7

For the revenue function $$R(p) = -6p^2$ + 600p$$, what price $$p$$ maximizes the revenue?

Accepted Answer

$$p = 50$$

Question 8

Given the function $$h(x) = 3x^2$ - 12$$, what are the zeros of the function as ordered pairs?

Accepted Answer

$$(2, 0)$$ and $$(-2, 0)$$

Question 9

Solve the inequality $$x^2 - 1$$ \u003c 0$$ and express the solution in interval notation.

Accepted Answer

$$(-1, 1)$$

Question 10

An astronaut on the moon throws a baseball upward. The height $$s (in $$feet) after $$t$$ seconds is given by $$s = -2.7t^2$ + 30t + 6.5. $$After how many seconds is the ball 22 feet above the moon’s surface? (Round to the nearest hundredth.)

Accepted Answer

$$0.56$$ seconds and $$7.94$$ seconds

Question 11

Given $$f(x) = (x-2)^2$ - 16$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -16)$$

Question 12

Solve the inequality $$|1 - 2x| - 4 \u003c -1$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -2.5) \cup (2.5, \infty)$$

Question 13

Find the equation of the quadratic function with vertex $$(2, -3)$$ that passes through the point $$(0, 7). $$Which of the following is correct (in vertex form)?

Accepted Answer

$$f(x) = 2.5(x-2)^2$ - 3$$

Question 14

For the function $$g(x) = x^2$ + x - 6$$, what are the $$x-$$intercepts as ordered pairs?

Accepted Answer

$$(2, 0)$$ and $$(-3, 0)$$

Question 15

Solve the inequality $$|3x + 4| \geq 2$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -2) or$$ $$(2, \infty)$$

Question 16

Given the quadratic $$h(x) = 3x^2$ - 5x + 1$$, what is the $$y-$$intercept as an ordered pair?

Accepted Answer

$$(0, 1)$$

Question 17

For the function $$g(x) = 4x^2$ - x + 2$$, which of the following best describes the graph?

Accepted Answer

Opens upward, vertex at $$\left(\frac{1}{8}, \frac{15}{8}\right)$$

Question 18

A company wants to earn at least $$12,600 in revenue. Using the revenue function R(p$$) = $$-6p^2 + 600p$, what is the range of prices p$ (rounded to the nearest cent) that will achieve this goal?

Accepted Answer

$$p \in [30, 70]$$

Question 19

For the moon baseball problem, when will the ball be at least 34 feet above the moon’s surface? (Give your answer as a compound inequality, rounded to the nearest hundredth.)

Accepted Answer

$$0.12 \u003c t \u003c 11.98$$

Question 20

Solve the equation $$2 + \frac{12}{-2x} = x. $$What is the solution set?

Accepted Answer

$$\left\{-3, 2\right\}$$

College Algebra Exam 2 Review: Step-by-Step Guidance

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