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: 49


The vertex form of the function is $y=2(x-7)^{2}+1.$ The vertex is $(7,1)$.

Work Step by Step

$ y=2x^{2}-28x+99\qquad$ ...factor out $2$ from the first two terms. $ y=2(x^{2}-14x)+99\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-14}{2})^{2}=7^{2}=49\qquad$ ...complete the square by adding$ 2\cdot 49$ to each side of the expression $ y+2\cdot 49=2(x^{2}-14x)+99+2\cdot 49\qquad$ ... ...factor out $2$ from the first and third term on the right side of the expression. $ y+98=2(x-14x+49)^{2}+99\qquad$ ... write $x-14x+49$ as a binomial squared. $ y+98=2(x-7)^{2}+99\qquad$ ...solve for $y$ by adding $-98$ to each side $ y+98-98=2(x-7)^{2}+99-98\qquad$ ...simplify. $y=2(x-7)^{2}+1$ 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, $h=7,\ k=1$, so the vertex is $(7,1)$
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