Question 1

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 2

Given the quadratic equation $2x^2 + 3x - 2 = 0$, what are the values of $a$, $b$, and $c$ to use in the quadratic formula?

Accepted Answer

$a = 2, b = 3, c = -2$

Question 3

What is the discriminant of the quadratic equation $x^2 - 4x + 4 = 0$?

Accepted Answer

$b^2 - 4ac = (-4)^2 - 4(1)(4) = 0$

Question 4

How many real solutions does the equation $x^2 + 2x + 5 = 0$ have?

Accepted Answer

No real solutions

Question 5

Which step is NOT part of solving a quadratic equation using the quadratic formula?

Accepted Answer

Factor the equation

Question 6

If the discriminant $b^2 - 4ac$ is negative, what type of solutions does the quadratic equation have?

Accepted Answer

Two imaginary solutions

Question 7

Solve $x^2 + 4x + 3 = 0$ using the quadratic formula.

Accepted Answer

$x = -1, x = -3$

Question 8

A ball is thrown upward and its height in meters after $t$ seconds is given by $h = -5t^2 + 20t + 1$. When does the ball hit the ground? (Solve for $t$ when $h = 0$ using the quadratic formula.)

Accepted Answer

$t = 4.04$ or $t = -0.04$

Question 9

Which of the following equations has exactly one real solution?

Accepted Answer

$x^2 - 6x + 9 = 0$

Question 10

Given $4x^2 + 4x + 1 = 0$, what is the value of the discriminant and what does it indicate about the solutions?

Accepted Answer

Discriminant is $0$, one real solution

Question 11

If $x^2 + 2x + 1 = 0$, what are the solutions using the quadratic formula?

Accepted Answer

$x = -1$

Question 12

Which of the following best describes the role of the discriminant in the quadratic formula?

Accepted Answer

It determines the number and type of solutions

Question 13

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

Accepted Answer

$x = 1, x = \frac{3}{2}$

Question 14

A company models its profit with $P(x) = -2x^2 + 8x + 10$. For what values of $x$ does the profit equal zero?

Accepted Answer

$x = -1, x = 5$

Question 15

Which of the following is a necessary first step before applying the quadratic formula to solve $3x^2 = 7x - 2$?

Accepted Answer

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

The Quadratic Formula and the Discriminant

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