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 - Quiz for Lessons 4.5-4.7 - Page 291: 14


The vertex form of the function is $y=(x-(-7))^{2}+(-4).$ The vertex is $(-7,-4)$.

Work Step by Step

$ y=x^{2}+14x+45\qquad$ ...write in form of $x^{2}+bx=c$ (add $-45$ to each side). $ y-45=x^{2}+14x\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{14}{2})^{2}=(7)^{2}=49\qquad$ ...complete the square by adding $49$ to each side of the expression $ y-45+49=x^{2}+14x+49\qquad$ ... write $x^{2}+14x+49$ as a binomial squared. $ y+4=(x+7)^{2}\qquad$ ...add $-4$ to each side of the expression $ y=(x+7)^{2}-4\qquad$ ...write in vertex form $y=a(x-h)^{2}+k$. $y=(x-(-7))^{2}+(-4)$ 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, $h=-7,\ k=-4$, so the vertex is $(-7,-4)$
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