Graphs

Graphs

Site: TBAISD Moodle
Course: Michigan Algebra I Preview 2012
Book: Graphs
Printed by: Guest user
Date: Saturday, July 20, 2019, 02:41 PM

Table of contents

From A Graph

The steps to model a polynomial function from a graph are very similar to the steps used when given a table. First, determine the zeros of the function by looking at the graph. Second, turn each zero into a factor of the function. Finally, determine the factored form of the polynomial.

Example 1 Determine the function that models the graph below:

ModelGraphEx1-1

Step 1. Determine the zeros of the function.

(-1, 0), (0, 0), (5, 0)

Step 2. Turn each zero into a factor of the function.

Since x = -1, then (x + 1) is a factor of the polynomial.

Since x = 0, then (x) is a factor of the polynomial.

Since x = 5, then ( x - 5) is a factor of the polynomial.

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Example 1 Continued

Step 3. Determine the factored form of the polynomial by using another point from the graph. Substitute the point in for (x, y) and solve for the value of a.

y = a (x + 1)(x)(x - 5); point (4, -40)

-40 = a (4 + 1)(4)(4 - 5)

-40 = a (5)(4)(-1)

-40 = a (-20)

2 = a

y = 2 ( x + 1)( x )( x - 5)

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Example 2

Determine the function that models the graph below:

ModelGraphEx2

Step 1. Determine the zeros of the function.

(-5, 0), (0, 0), (2, 0), (3, 0)

Step 2. Turn each zero into a factor of the function.

Since x = -5, then (x + 5) is a factor of the polynomial.

Since x = 0, then (x) is a factor of the polynomial.

Since x = 2, then (x - 2) is a factor of the polynomial.

Since x = 3, then (x - 3) is a factor of the polynomial.

Step 3. Determine the factored form of the polynomial by using another point from the graph. Substitute the point in for (x, y) and solve for the value of a.

y = a (x + 5)(x)(x - 2)(x - 3); point (-2, -60)

-60 = a (-2 + 5)(-2)(-2 - 2)(-2 - 3)

-60 = a (3)(-2)(-4)(-5)

-60 = a (-120)

.5 = a

y = .5 ( x + 5)( x )( x - 2)( x - 3)

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Practice

Polynomials Equations Worksheet

Answer Key

Polynomials Equations Answer Key

Source

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