Question 1

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$, where a$$ 
eq 0$$?

Accepted Answer

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

Question 2

A ball is thrown upward from the ground and its height in meters after $$t$$ seconds is given by $$h = -5t^2$ + 20t. $$After how many seconds will the ball hit the ground again? (Use the quadratic formula.)

Accepted Answer

$$t = 0 or$$ $$t = 4$$

Question 3

Given the equation $$3x^2 - 2x = 7$, what are the values of a$, b$, and c$ to use in the quadratic formula?

Accepted Answer

$$a = 3$$, $$b = -2$$, $$c = -7$$

Question 4

Solve $$x^2 - 5x - 14 = 0$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = 7$$ and $$x = -2$$

Question 5

Which of the following expressions correctly represents the two solutions to $$2x^2 + 9x + 5 = 0$ using the quadratic formula?

Accepted Answer

$$x = \dfrac{-9 \pm \sqrt{81 - 40}}{4}$$

Question 6

A rectangular garden has an area of $$14 m$^2$$ and its length is $$5 m $$more than its width. Which quadratic equation can be used to find the width $$w$$?

Accepted Answer

$$w^2 + 5w - 14 = 0$

Question 7

Solve $$9x^2 - 6x + 1 = 0$ using the quadratic formula. What is the solution?

Accepted Answer

$$x = \dfrac{1}{3}$$

Question 8

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

Accepted Answer

It determines the number and type of solutions for the quadratic equation.

Question 9

A company’s profit $$P (in $$thousands of dollars) after $$x$$ years is modeled by $$P = -2x^2$ + 8x + 10. $$After how many years will the profit be zero? (Round to the nearest thousandth if necessary.)

Accepted Answer

$$x = -1 or$$ $$x = 5$$

Question 10

Given the expression $$\dfrac{6 \pm \sqrt{75}}{2}$$, what are the two numbers represented after simplifying?

Accepted Answer

$$3 + \dfrac{5\sqrt{3}}{2}$$ and $$3 - \dfrac{5\sqrt{3}}{2}$$

Question 11

Solve $$5x^2 - 4x = 2$ using the quadratic formula. What are the solutions?

Accepted Answer

$$x = 1.2$$ and $$x = -0.333$$

Question 12

A quadratic equation has no real solutions. Which of the following must be true about its discriminant?

Accepted Answer

$$b^2 - 4ac$$ \u003c 0$$

Question 13

Solve $$x^2 + 6x - 1 = 4$ using the quadratic formula. What are the solutions rounded to three decimal places?

Accepted Answer

$$x = -2.162$$ and $$x = -3.838$$

Question 14

Which of the following is a common mistake when using the quadratic formula?

Accepted Answer

Forgetting to divide the entire numerator by $$2a$$

Question 15

A projectile is launched and its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -4.9t^2$ + 10t + 2. $$When will the projectile hit the ground? (Round to three decimal places.)

Accepted Answer

$$t = 2.236$$ 	ext{ seconds}$

Question 16

If $$x = \dfrac{-1 \pm \sqrt{25}}{4}$$, what are the two solutions?

Accepted Answer

$$x = 1$$ and $$x = -1.5$$

Question 17

Solve $$3x^2 = 3x + 5$ using the quadratic formula. What are the solutions rounded to three decimal places?

Accepted Answer

$$x = 2.215$$ and $$x = -0.748$$

Question 18

Which of the following real-life situations can be modeled by a quadratic equation?

Accepted Answer

The path of a thrown baseball

Question 19

Given $$5x^2 - 4x - 2 = 0$, what is the value of the discriminant?

Accepted Answer

$$(-4)^2 - 4$$ \cdot 5 \cdot (-2) = 16 + 40 = 56$$

Section 8.2: The Quadratic Formula – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards