Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. For this exercise, make the leading coefficient be 1 or - 1. An equation for the polynomial function is f(x) =.

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.2: Polynomial Functions
Problem 8E
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Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. For
this exercise, make the leading coefficient be 1 or 1.
Af(x)
10
10
15
10
10
An equation for the polynomial function is f(x) =
%3D
Transcribed Image Text:Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. For this exercise, make the leading coefficient be 1 or 1. Af(x) 10 10 15 10 10 An equation for the polynomial function is f(x) = %3D
Expert Solution
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the graph crosses the x-axis at x=0, x=2 and x=3

so the factored form of the polynomial is given by 

f(x)=a(x-0)(x-2)(x-3)

f\left(x\right)=ax\left(x-2\right)\left(x-3\right)

f\left(x\right)=ax\left(x^2-2x-3x+6\right)

f\left(x\right)=ax\left(x^2-5x+6\right)

f\left(x\right)=a\left(x^3-5x^2+6x\right)

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