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

Question 1

Solve the quadratic equation $$x^2 - 3x + 2 = 0$ by factoring.

Accepted Answer

$$x = 1$$ and $$x = 2$$

Question 2

Solve $$(x - 2)^2$ = 9$$ for $$x.$$

Accepted Answer

$$x = 5$$ and $$x = -1$$

Question 3

Find the vertex of $$h(x) = x^2$ - 10x + 25.$$

Accepted Answer

$$(5, 0)$$

Question 4

Find the vertex of $$f(x) = 3x^2$ - 12x + 7.$$

Accepted Answer

$$(2, -5)$$

Question 5

For $$f(x) = -3(x - 5)^2$ - 1$$, what is the direction in which the parabola opens?

Accepted Answer

Downward

Question 6

For $$g(x) = 2(x + 2)^2$ - 2$$, what are the coordinates of the vertex?

Accepted Answer

$$(-2, -2)$$

Question 7

For $$f(x) = 2x^2$ + 4$$, what is the y-intercept?

Accepted Answer

$$(0, 4)$$

Question 8

Use synthetic division to divide $$2x^5$$ + $$x^4$$ - $$10x^3$$ + $$2x^2 + x - 16$ by (x + 2$$)$$. What is the remainder?

Accepted Answer

$$-14$$

Question 9

Use synthetic division to divide $$10x^3$$ - $$14x^2 + 2x - 9$ by (x - 1$$)$$. What is the remainder?

Accepted Answer

$$-11$$

Question 10

Use synthetic division to divide $$x^4 - 4$ by (x - 2$$)$$. What is the remainder?

Accepted Answer

$$12$$

Question 11

List all possible rational zeros for $$g(x) = x^3$ - 3x^2$ - 13x + 15$$ using the Rational Root Theorem.

Accepted Answer

$$\pm1, \pm3, \pm5, \pm15$$

Question 12

Find all rational zeros of $$f(x) = -x^3$ - 5x^2$ + x + 5.$$

Accepted Answer

$$x = -5, x = -1, x = 1$$

Question 13

Which of the following best describes the end behavior of $$f(x) = -x^3$ - 5x^2$ + x + 5$$?

Accepted Answer

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

Question 14

A projectile is launched and its height is modeled by $$h(x) = -3(x - 5)^2$ - 1. $$What is the maximum height reached?

Accepted Answer

$$-1$$

Question 15

If $$g(x) = 2(x + 2)^2$ - 2$$, what are the x-intercepts?

Accepted Answer

$$x = -2 \pm \sqrt{1}$$

Question 16

For $$f(x) = 2x^2$ + 4$$, does the parabola open upward or downward?

Accepted Answer

Upward

Question 17

Which method is most efficient for solving $$x^2 - 3x + 2 = 0$?

Accepted Answer

Factoring

Question 18

If $$f(x) = 3x^2$ - 12x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-5$$

Question 19

For $$g(x) = x^3$ - 3x^2$ - 13x + 15$$, which of the following is a rational zero?

Accepted Answer

$$x = 1$$

Question 20

If $$f(x) = -x^3$ - 5x^2$ + x + 5$$, what is the y-intercept?

Accepted Answer

$$(0, 5)$$

Quadratic Equations and Polynomial Functions: Study Guide

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