Question 1

Which of the following is the correct general form of a quadratic equation in one variable?

Accepted Answer

$$ax^2 + bx + c = 0$

Question 2

A quadratic equation can have up to how many real solutions?

Accepted Answer

Two

Question 3

Which property states that if $$ab = 0$$, then either $$a = 0 or$$ $$b = 0$$?

Accepted Answer

Zero-Factor Property

Question 4

Solve the equation $$x^2 - 4x + 4 = 0$ using factoring. What are the solutions?

Accepted Answer

$$x = 2$$

Question 5

Which method is most appropriate for solving $$x^2 = 25$?

Accepted Answer

Square-Root Property

Question 6

What is the solution to $$x^2 = -9$?

Accepted Answer

$$x = \pm 3i$$

Question 7

Given the quadratic equation $$2x^2 - 4x = 6$, which is the first step to solve it by factoring?

Accepted Answer

Move all terms to one side to set the equation equal to zero

Question 8

What is the discriminant of the quadratic equation $$x^2 - 6x + 9 = 0$?

Accepted Answer

$$0$$

Question 9

If the discriminant $$b^2 - 4ac$ of a quadratic equation is negative, what does this indicate about the solutions?

Accepted Answer

There are two complex solutions

Question 10

Solve $$x^2 - 2x - 8 = 0$ by factoring.

Accepted Answer

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

Question 11

Which of the following is the quadratic formula?

Accepted Answer

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

Question 12

A student is solving $$x^2 + 6x + 5 = 0$ by completing the square. What should be added to both sides after moving the constant term?

Accepted Answer

$$9$$

Question 13

Which of the following real-world scenarios can be modeled by a quadratic equation?

Accepted Answer

The height of a ball thrown upward as a function of time

Question 14

What is the solution to $$3x^2 = 12$ using the square-root property?

Accepted Answer

$$x = \pm 2$$

Question 15

Which step is necessary when completing the square for $$x^2 + 8x = 20$?

Accepted Answer

Add $$16 to $$both sides

Question 16

A chemical reaction's rate is modeled by $$t^2 - 4t + 3 = 0$. What are the possible values of t$?

Accepted Answer

$$t = 1, t = 3$$

Question 17

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

Accepted Answer

Linear regression

Question 18

If $$x^2 + 2x + 1 = 0$, what is the nature of its solutions?

Accepted Answer

One real repeated solution

Question 19

A medical dosage is modeled by $$d^2 - 5d + 6 = 0$. What is the correct dosage d$?

Accepted Answer

$$d = 2, d = 3$$

Question 20

Which of the following best describes the discriminant $$b^2 - 4ac$?

Accepted Answer

It determines the number and type of solutions of a quadratic equation

Quadratic Equations in One Variable: Methods and Applications

Study Guide - Practice Questions