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: 43


The vertex form of the function is $y=(x-(-6))^{2}+1.$ The vertex is $(-6,1)$.

Work Step by Step

$ y=x^{2}+12x+37\qquad$ ...prepare to complete the square. $ y+?=x^{2}+12x+?+37\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{12}{2})^{2}=(6)^{2}=36\qquad$ ...complete the square by adding $36$ to each side of the expression $ y+36=x^{2}+12x+36+37\qquad$ ... write $x^{2}+12x+36$ as a binomial squared. $ y+36=(x+6)^{2}+37\qquad$ ...add $-36$ to each side of the expression $ y+36-36=(x+6)^{2}+37-36\qquad$ ...simplify. $ y=(x+6)^{2}+1\qquad$ ...write in vertex form $y=a(x-h)^{2}+k$. $y=(x-(-6))^{2}+1$ 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, $h=-6,\ k=1$, so the vertex is $(-6,1)$
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