Question 1

Which of the following is the standard form of a quadratic equation?

Accepted Answer

$ax^2 + bx + c = 0$

Question 2

Given the quadratic equation $2x^2 - 4x - 6 = 0$, what is the value of the discriminant?

Accepted Answer

$(-4)^2 - 4(2)(-6) = 16 + 48 = 64$

Question 3

How many real solutions does the equation $x^2 + 4x + 8 = 0$ have?

Accepted Answer

0 real solutions

Question 4

Which method is most appropriate for solving $x^2 - 9 = 0$?

Accepted Answer

Factoring (difference of squares)

Question 5

Solve $x^2 - 6x + 9 = 0$ by factoring.

Accepted Answer

$x = 3$

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

There is one real solution

Question 8

Solve $2x^2 = 10$ using the square root property.

Accepted Answer

$x = \pm \sqrt{5}$

Question 9

Which of the following best describes the process of completing the square for $x^2 + 6x + 5 = 0$?

Accepted Answer

Add $9$ to both sides to form $(x+3)^2 = 4$

Question 10

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

Accepted Answer

$t = 4.04$ or $t = -0.04$ (only $t = 4.04$ is valid)

Question 11

Which of the following equations can be solved by factoring as a difference of squares?

Accepted Answer

$x^2 - 16 = 0$

Question 12

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

Accepted Answer

$x = -1 \pm i$

Question 13

If $x^2 + 4 = 0$, what are the solutions?

Accepted Answer

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

Question 14

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

Accepted Answer

One real solution

Question 15

A chemical reaction's rate is modeled by $t^2 - 6t + 8 = 0$, where $t$ is time in seconds. When does the reaction reach a rate of zero?

Accepted Answer

$t = 2$ or $t = 4$

Question 16

Which of the following is NOT a valid step in the process of completing the square?

Accepted Answer

Multiply both sides by the leading coefficient if it is not 1

Question 17

Solve $x^2 + 6x + 5 = 0$ by factoring.

Accepted Answer

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

Question 18

If $x^2 + bx + c = 0$ has two imaginary solutions, what must be true about the discriminant?

Accepted Answer

$b^2 - 4ac < 0$

Question 19

A ball is thrown upward and its height is modeled by $h = -16t^2 + 32t + 5$. When does it return to the ground?

Accepted Answer

$t = 2.13$\ (rounded)$

Quadratic Equations: Methods of Solution and the Discriminant

Study Guide - Practice Questions