Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - Guided Practice for Examples 6 and 7 - Page 287: 15


The vertex form of the function is $f(x)=(x-2)^{2}+(-8).$ The vertex is $(2,-8)$.

Work Step by Step

$ f(x)=x^{2}-4x-4\qquad$ ...prepare to complete the square. $ f(x)+?=(x^{2}-4x+?)-4\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-4}{2})^{2}=(-2)^{2}=4\qquad$ ...add $4$ to each side of the expression $ f(x)+4=(x^{2}-4x+4)-4\qquad$ ... write $x^{2}-4x+4$ as a binomial squared. $ f(x)+4=(x-2)^{2}-4\qquad$ ...add $-4$ to each side of the expression $ f(x)+4-4=(x-2)^{2}-4-4\qquad$ ...simplify. $ f(x)=(x-2)^{2}-8\qquad$ ...write in vertex form $y=a(x-h)^{2}+k$. $f(x)=(x-2)^{2}+(-8)$ The vertex form of a quadratic function is $y=a(x-h)^{2}+k$ where $(h,k)$ is the vertex of the function's graph. Here, $h=2,\ k=-8$, so the vertex is $(2,-8)$
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