Finding Zeros
| Site: | Harrison |
| Course: | Michigan Algebra I Sept. 2012 |
| Book: | Finding Zeros |
| Printed by: | Guest user |
| Date: | Thursday, 21 November 2024, 2:44 PM |
Description
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.
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
Models
Finding the zero of a graph provides useful information.
Example
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
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
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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)