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 $$x^2$$ \u003c 9$$.

Accepted Answer

$$-3 \u003c x \u003c 3$$

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

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