Graphing

Graphing

Site: TBAISD Moodle
Course: Michigan Algebra I Preview 2012
Book: Graphing
Printed by: Guest user
Date: Saturday, August 8, 2020, 05:26 AM

Table of contents

Introduction

There are numerous ways to solve quadratic equations. This unit will cover graphing, using square roots, factoring, the quadratic formula, and completing the square.

When solving a quadratic equation, there will be two, one or no real solutions. When there are no real solutions the solutions can be represented by the imaginary number i. Since GraphingIntro1, the complex number i is defined as GraphingIntro2. This number can help to define any square root of a negative number.

Example 1

Simplify GraphingIntro3

GraphingIntro4, the square roots can be simplified to 4i.

Example 2

Simplify GraphingIntro5

GraphingIntro6, the square roots can be simplified toGraphingIntro7.


Listen

Solutions

In general, graphing provides a good way of approximating solutions to quadratic equations as long as the graph has x-intercepts. When a quadratic equation is written in the form ax2 + bx + c = 0, the solutions will be the value(s) of x when y = 0. Another name for these solutions are x-intercepts or roots. A graphing calculator can be used to estimate these solutions. Remember, quadratic equations can have two, one, or no real solutions. Therefore, the graphs will have two, one, or no x -intercepts.

Listen

Example

Find the solutions to the equation 2x2 + 4x - 3 = 0 by graphing.

Step 1. Rewrite the equation by substituting a y in the place of the zero.

y = 2x2 + 4x - 3

Step 2. Use a graphing calculator to make a graph of the function.

SolutionsEx1

Step 3. Does the graph have two, one or no x-intercepts (solutions)?

This graph has 2 x-intercepts, therefore look for 2 solutions to the equation.

Step 4. Use the calculate zeros command to calculate the solutions (x-intercepts) of the equation.

SolutionsEx2

*Note: Sometimes the solutions will appear on the table. Use the table function of a graphing calculator and find the values on the table where the y -coordinate is zero.

Listen

Video Lesson

To learn how to solve quadratic equations by graphing, select the following link:

Solving Quadratics by Graphing

Guided Practice

To solidify your understanding of solving quadratics by graphing, 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 Graphing Worksheet

Answer Key

Solve by Graphing Answer Key

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_05_homeworkhelp.html (accessed 7/18/2010).