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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