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: 13


The vertex form of the function is $y=(x-2)^{2}+5.$ The vertex is $(2,5)$.

Work Step by Step

$ y=x^{2}-4x+9\qquad$ ...write in form of $x^{2}+bx=c$ (add $-9$ to each side). $ y-9=x^{2}-4x\qquad$ ...square half the coefficient of $x$. $(\displaystyle \frac{-4}{2})^{2}=(-2)^{2}=4\qquad$ ...complete the square by adding $4$ to each side of the expression $ y-9+4=x^{2}-4x+4\qquad$ ... write $x^{2}-4x+4$ as a binomial squared. $ y-5=(x-2)^{2}\qquad$ ...add $5$ to each side of the expression $ y=(x-2)^{2}+5\qquad$ ...write in vertex form $y=a(x-h)^{2}+k$. 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, $h=2,\ k=5$, so the vertex is $(2,5)$
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