## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Skill Practice - Page 289: 49

#### Answer

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 $(7,1)$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.