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 - 4.7 Exercises - Skill Practice - Page 289: 41


The vertex form of the function is $y=(x-4)^{2}+3.$ The vertex is $(4,3)$.

Work Step by Step

$ y=x^{2}-8x+19\qquad$ ...prepare to complete the square. $ y+?=x^{2}-8x+?+19\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-8}{2})^{2}=(-4)^{2}=16\qquad$ ...complete the square by adding $16$ to each side of the expression $ y+16=x^{2}-8x+16+19\qquad$ ... write $x^{2}-8x+16+19$ as a binomial squared. $ y+16=(x-4)^{2}+19\qquad$ ...add $-16$ to each side of the expression $ y+16-16=(x-4)^{2}+19-16\qquad$ ...simplify. $y=(x-4)^{2}+3$ 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, $h=4,\ k=3$, so the vertex is $(4,3)$
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