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: 47


The vertex form of the function is $y=2(x+6)^{2}-47.$ The vertex is $(-6,-47)$.

Work Step by Step

$ y=2x^{2}+24x+25\qquad$ ...factor out $2$ from the first two terms. $ y=2(x^{2}+12x)+25\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{12}{2})^{2}=6^{2}=36\qquad$ ...complete the square by adding $ 2\cdot 36$ to each side of the expression $ y+2\cdot 36=2(x^{2}+12x)+25+2(36)\qquad$ ... ...factor out $2$ from the first and third term on the right side of the expression. $ y+72=2(x+12x+36)^{2}+25\qquad$ ... write $x+12x+36$ as a binomial squared. $ y+72=2(x+6)+25\qquad$ ...solve for $y$ by adding $-72$ to each side $ y+72-72=2(x+6)^{2}+25-72\qquad$ ...simplify. $y=2(x+6)^{2}-47$ 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, $h=-6,\ k=-47$, so the vertex is $(-6,-47)$
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