Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 4 - Quadratic Functions - 4.5 Solving Equations by Factoring - 4.5 Exercises: 73

Answer

$\color{blue}{f(x)=x^2-6x+8}$

Work Step by Step

RECALL: The zeros of the quadratic function $f(x) =(x+a)(x+b)=0$ are $x=-a$ and $x=-b$. The given quadratic function has the zeros $x=2$ and $x=4$. Using the rule mentioned in the recall part above, then the function is: $f(x)=[x+(-2)][x+(-4)] \\f(x)=(x-2)(x-4) \\f(x)=x^2+x(-4) - 2(x) - 2(-4) \\f(x)=x^2-4x-2x+8 \\\color{blue}{f(x)=x^2-6x+8}$
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