Question 1

Which of the following equations is a quadratic equation written in standard form?

Accepted Answer

$$2x^2 + 5x - 3 = 0$

Question 2

Given the equation $$-4x^2 + x = 8$, what are the values of a$, b$, and c$ when written in standard form ax^2$ + bx + c = 0$$?

Accepted Answer

$$a = -4,\ b = 1,\ c = -8$$

Question 3

Which factoring formula is used to factor $$x^2 - 9$?

Accepted Answer

$$(a + b)(a - b) = a^2$ - b^2$

Question 4

Solve the quadratic equation $$x^2 + x - 6 = 0$ by factoring.

Accepted Answer

$$x = -3,\ x = 2$$

Question 5

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t + 2. $$After how many seconds does the ball hit the ground? (Solve for $$t$$ when $$h = 0$$ using the quadratic formula.)

Accepted Answer

$$t = 4.04,\ t = -0.10$$

Question 6

Which method is most appropriate to solve $$(x + 2)^2$ = 9$$?

Accepted Answer

Square root property

Question 7

Solve $$3x^2 + 12x = 0$ by factoring.

Accepted Answer

$$x = 0,\ x = -4$$

Question 8

What is the discriminant of $$x^2 + 8x + 16 = 0$ and what does it tell you about the solutions?

Accepted Answer

Discriminant is $$0$$; one real solution

Question 9

Solve $$2x^2 - 16 = 0$ using the square root property.

Accepted Answer

$$x = 2,\ x = -2$$

Question 10

Which of the following best describes the number and type of solutions for $$4x^2 + x + 2 = 0$?

Accepted Answer

Two complex solutions

Question 11

A company’s profit $$P (in $$thousands of dollars) is modeled by $$P = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). For what values of $$x$$ does the company break even? (Solve for $$P = 0.)$$

Accepted Answer

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

Question 12

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 13

Solve $$x^2 + 6x + 1 = 0$ by completing the square.

Accepted Answer

$$x = -3 + 2\sqrt{2},\ x = -3 - 2\sqrt{2}$$

Question 14

Which of the following equations would be best solved by factoring?

Accepted Answer

$$x^2 - 9x = -20$

Question 15

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what can you conclude about the solutions?

Accepted Answer

There are two complex solutions

Question 16

Solve $$x^2 + 3x - 5 = 0$ using the quadratic formula.

Accepted Answer

$$x = \frac{-3 \pm \sqrt{29}}{2}$$

Question 17

Which of the following is NOT a valid method for solving all quadratic equations?

Accepted Answer

Factoring (when the equation is not factorable)

Question 18

A projectile is launched from the ground and its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -4.9t^2$ + 24t. $$When will the projectile return to the ground? (Solve for $$t$$ when $$h = 0.)$$

Accepted Answer

$$t = 0,\ t = 4.90$$

Quadratic Equations and Inequalities: College Algebra Study Guide

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