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Quadratic Formula

Site: Clare-Gladwin RESD
Course: Michigan Algebra I
Book: Quadratic Formula
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Date: Wednesday, January 15, 2025, 3:31 PM

Description

Quadratic Formula

Table of contents

The Formula

Unlike some of the other techniques discussed, the quadratic formula is a way to solve any quadratic equation of the form y = ax2 + bx + c. Substituting the values of a, b, and c into the equation below and simplifying will result in the solutions of the equation.

The Quadratic Formula is: QuadForm.

To see how the formula can be derived by completing the square of y = ax2 + bx + c, select the link below:

Quadratic Formula


Example 1

Solve the quadratic equation x2 - x - 12 = 0 by using the quadratic formula.

Step 1. Determine the values of a, b, and c.

For this equation a = 1, b = -1, and c = -12.

Step 2. Substitute the values of a, b, and c into the formula.

QuadFormEx1-1

Step 3. Simplify.

QuadFormEx1-2

Example 2

Solve the quadratic equation 2x2 + 3x + 12 = 0 by using the quadratic formula.

Step 1. Determine the values of a, b, and c.

For this equation a = 2, b = 3, and c = 12.

Step 2. Substitute the values of a, b, and c into the formula.

QuadFormEx2-1

Step 3. Simplify.

QuadFormEx2-2


Video Lessons

To learn how to use the quadratic formula to solve quadratics, select one of the following links:

Solve Quadratics by Quadratic Formula #1

Solve Quadratics by Quadratic Formula #2

Video Lesson

To review all the ways to solve quadratics, select the following link:

Solving Quadratics

Guided Practice

To solidify your understanding of the quadratic formula, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Practice

Solve by Quadratic Formula Worksheet

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Answer Key

Solve by Quadratic Formula Answer Key

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Sources

Embracing Mathematics, Assessment & Technology in High Schools; A Michigan Mathematics & Science Partnership Grant Project

Holt, Rinehart & Winston, "Quadratic Equations and Functions." http://my.hrw.com/math06_07/nsmedia/homework_help/alg1/alg1_ch09_09_homeworkhelp.html (accessed 8/18/2010).

Holt, Rinehart & Winston, "Quadratic Functions with Complex Zeros." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg2/player.html?contentSrc=7109/7109.xml (accessed 8/18/2010).

Holt, Rinehart & Winston, "Using the Quadratic Formula." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=6379/6379.xml (accessed 8/18/2010).

Holt, Rinehart & Winston, "Solving Using Different Methods." http://my.hrw.com/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7960/7960.xml (accessed 8/18/2010).

Hot Math, "Quadratic Formula." http://hotmath.com/help/gt/genericalg1/ section_10_3.html (accessed 07/16/2010).

SOSMathematics, "Quadratic Equation: Quadratic Formula." http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html (accessed 07/24/2010).