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Finding Zeros

Site: St. Louis
Course: Michigan Algebra I Sept. 2012
Book: Finding Zeros
Printed by: Guest user
Date: Saturday, April 27, 2024, 8:03 PM

Description

Table of contents

Introduction

Finding the zero(s) of a function is the result of setting the function equal to zero, or f(x) = 0. Since f(x) is the same as y, the ordered pair will be (x, f(x)) = (x, y) = (x, 0). The function crosses the x-axis when y = 0, therefore the zero of a function describes the x-intercept(s). A linear equation has no zeros or one zero.

Example Find the zero (or x-intercept) of f(x) = -2x + 4.

Step 1. Set the equation equal to 0.

-2x + 4 = 0

Step 2. Solve the equation.

-2x + 4 - 4 = 0 - 4
-2x = -4
-2 -2

x = 2

Therefore, the zero of the function is (2, 0).

Graphically

To find the zero of a graph of a linear equation, locate the x-intercept.

Example Find the zero of the function graphed below.

zeros_graphically

The x-intercept, and therefore the zero, is (-1.5, 0).


No Zeros

If the graph is a horizontal line, then it will not intersect the x-axis and does not have a zero.

f(x) = 4

zeros_noZeros

Models

Finding the zero of a graph provides useful information.

Example

zeros_models

In this graph, the x-intercept is (150, 0). This means, that when 150 items are demanded the price will be $0.00.


Example 2

zeros_model_ex2

Thex -intercept of (0, 0) means at 0 hours, the object being measured moved 0 km.


Video Lesson

To learn more about finding zeros, watch the video below.


Practice

Linear Zeros Worksheet

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Answer Key

Linear Zeros Answer Key

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Sources

Biz/ed, "From Basic to Involved Mathematics." http://www.bized.co.uk/learn/economics/maths/graphs.htm (accessed August 17, 2010).

Bourne, M. "Differentiation (Finding Derivatives). "http://www.intmath.com/Differentiation/Differentiation-intro.php (accessed August 17, 2010).

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

Gulati, Vinni. "Linear Graphs." http://www.staff.vu.edu.au/mcaonline/units/graphs/linear.html (accessed August 17, 2010)

Home Schooling Unlimited, "Graphing Linear Functions ." http://www.hsunlimited.com/math-lessons/topic/Graphing-Linear-Functions (accessed August 17, 2010)