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: 14


The vertex form of the function is $y=(x-(-3))^{2}+(-6).$ The vertex is $(-3,-6)$.

Work Step by Step

$ y=x^{2}+6x+3\qquad$ ...prepare to complete the square. $ y+(?)=x^{2}+6x+(?)+3\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{6}{2})^{2}=3^{2}=9\qquad$ ...add $9$ to each side of the expression $ y+9=x^{2}+6x+9+3\qquad$ ... write $x^{2}+6x+9$ as a binomial squared. $ y+9=(x+3)^{2}+3\qquad$ ...add $-9$ to each side of the expression $ y+9-9=(x+3)^{2}+3-9\qquad$ ...simplify. $ y=(x+3)^{2}-6\qquad$ ...write in vertex form $y=a(x-h)^{2}+k$. $y=(x-(-3))^{2}+(-6)$ 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, $h=-3,\ k=-6$, so the vertex is $(-3,-6)$
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