Question 1

Which of the following equations is a quadratic equation in $$x$$?

Accepted Answer

$$x^2 + 3x - 7 = 0$

Question 2

What is the zero-product principle used for when solving quadratic equations?

Accepted Answer

To set each factor equal to zero after factoring, since if $$AB = 0$$, then $$A = 0 or$$ $$B = 0$$

Question 3

Solve the quadratic equation $$x^2 - 5x + 6 = 0$ by factoring.

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 4

Which of the following is the correct application of the square root property to solve $$x^2 = 25$?

Accepted Answer

$$x = \pm 5$$

Question 5

Solve $$5x^2 + 45 = 0$ using the square root property.

Accepted Answer

$$x = \pm 3i$$

Question 6

Complete the square for $$x^2 + 6x = 7$ and solve for x$.

Accepted Answer

$$x = -3 \pm 4$$

Question 7

Which formula is used to solve any quadratic equation $$ax^2 + bx + c = 0$?

Accepted Answer

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

Question 8

Given the quadratic equation $$2x^2 - 7x - 4 = 0$, what is the value of the discriminant and what does it indicate about the solutions?

Accepted Answer

Discriminant is $$81$$, indicating two real solutions

Question 9

A quadratic equation has a discriminant of zero. What does this tell you about its solutions?

Accepted Answer

There is one real (repeated) solution

Question 10

Which of the following is the most efficient method to solve $$x^2 - 16 = 0$?

Accepted Answer

Square root property

Question 11

A woman’s normal systolic blood pressure $$P at $$age $$A is $$modeled by $$P = 0.01A^2$ + 0.05A + 107. If $$her blood pressure is $$115 mm Hg$$, which equation should you solve to find her age?

Accepted Answer

$$0.01A^2 + 0.05A + 107 = 115$

Question 12

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

Accepted Answer

There are two imaginary solutions

Question 13

Solve $$x^2 + 4x + 5 = 0$ using the quadratic formula.

Accepted Answer

$$x = -2 \pm i$$

Question 14

Which step is NOT part of solving a quadratic equation by factoring?

Accepted Answer

Divide both sides by $$x$$

Question 15

A ball is thrown upward and its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -5t^2$ + 20t + 1. $$When does the ball hit the ground?

Accepted Answer

$$t = 0 or$$ $$t = 4.05$$ seconds

Question 16

Which of the following best describes the equation $$x^2 + 2x + 1 = 0$?

Accepted Answer

It has one real (repeated) solution

Question 17

What is the solution set for $$2x^2 + x = 1$?

Accepted Answer

$$\left\{\frac{1}{2}, -1\right\}$$

Question 18

Which of the following is a real-world application of quadratic equations?

Accepted Answer

Modeling the trajectory of a projectile

Quadratic Equations: Methods, Properties, and Applications

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