As $x \to \infty$, $f(x) \to \infty$; as $x \to -\infty$, $f(x) \to -\infty$

Question 1

Solve the quadratic equation by factoring: $x^2 - 9x + 20 = 0$.

Accepted Answer

$x = 4$ or $x = 5$

Question 2

Which of the following is the correct solution to $3x^2 + 11x = 4$ by factoring?

Accepted Answer

$x = -4$, $x = \frac{1}{3}$

Question 3

Solve $10z^2 + 6z = 7$ using the quadratic formula.

Accepted Answer

$z = \frac{-3 \pm \sqrt{31}}{10}$

Question 4

Given $f(x) = -18 + 0.5x - \pi x^2$, what is the degree of the polynomial?

Accepted Answer

2

Question 5

Given $f(x) = -2x^2 - 16x - 31$, what is the vertex of the parabola?

Accepted Answer

$(-4, 1)$

Question 6

For the polynomial $f(x) = 2x^3 + 2x^2 - 9x + 4$, what is the maximum number of turning points?

Accepted Answer

2

Question 7

Completely factor $f(x) = x^4 - x^3 - 20x^2$ and state the zeros.

Accepted Answer

$x(x-5)(x+4)(x) = 0$; Zeros: $x = 0$ (multiplicity 2), $x = 5$, $x = -4$

Question 8

Use synthetic division to determine if $x + 6$ is a factor of $f(x) = x^3 - 11x^2 + 17x + 90$.

Accepted Answer

Yes, because the remainder is 0.

Question 9

Given $f(x) = 3x^2 - 8x + 15$, what is the domain of $f(x)$?

Accepted Answer

All real numbers

Question 10

Given the rational function $f(x) = \frac{x^2 - 4}{x^2 + 6x + 8}$, what are the vertical asymptotes?

Accepted Answer

$x = -4$ and $x = -2$

Question 11

Solve the inequality $x^2 < 9$.

Accepted Answer

$-3 < x < 3$

Question 12

Given $f(x) = 5x^3 + 6x^2 - 5x + 7$, what is the end behavior of the graph?

Accepted Answer

As $x 	o \infty$, $f(x) 	o \infty$; as $x 	o -\infty$, $f(x) 	o -\infty$

Question 13

For the quadratic function $f(x) = 4x^2 + 40x + 96$, what is the axis of symmetry?

Accepted Answer

$x = -5$

Question 14

Given $f(x) = -2x^2 - 16x - 31$, does the function have a maximum or minimum value, and what is it?

Accepted Answer

Maximum at $y = 1$

Question 15

Given $f(x) = x^3 + 3x^2 - 10x - 24$, what are the zeros of the function?

Accepted Answer

$x = -4$, $x = -2$, $x = 3$

Question 16

For the rational function $f(x) = \frac{3x}{x^2 - 4}$, what is the horizontal asymptote?

Accepted Answer

$y = 0$

Question 17

Solve the quadratic equation $x^2 - 3x = 8$.

Accepted Answer

$x = -2$, $x = 5$

Question 18

Given $f(x) = -2x + 32x - 1$, what is the degree of the polynomial?

Accepted Answer

1

Question 19

Use synthetic division to find $f(-3)$ for $f(x) = 2x^3 + 2x^2 + 4x + 8$.

Accepted Answer

$-10$

Question 20

Given $f(x) = x^2 + 8x + 15$, what are the solutions to $f(x) = 0$?

Accepted Answer

$x = -3$, $x = -5$

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

Study Guide - Practice Questions