Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - 4-6 Complete the Square - Practice and Problem-Solving Exercises - Page 238: 50

Answer

$y=2\left(x-\frac{3}{2}\right)^2-\frac{11}{2}$

Work Step by Step

\begin{align*} &y=(2x^2-6x)-1 &\text{Group the terms with variables together.}\\ &y=2(x^2-3x)-1 &\text{Factor out $2$.}\\ \end{align*} Recall: To complete the square of $y=a(x^2+bx)+c$, you add $\left(\dfrac{b}{2}\right)^2$ inside the parentheses and subtract $a\cdot \left(\dfrac{b}{2}\right)^2$ outside to obtain $y=a\left[x^2+bx +\color{blue}{\left(\dfrac{b}{2}\right)^2}\right]+c-\color{red}{a\left(\dfrac{b}{2}\right)^2}$ \begin{align*} &y=2\left[x^2-3x+\color{blue}{\left(\frac{-3}{2}\right)^2}\right]-1-\color{red}{2\left(\frac{-3}{2}\right)^2} &\text{Complete the square.}\\\\ &y=2\left[x^2-3x+\frac{9}{4}\right]-1-2\left(\frac{9}{4}\right) &\text{Simplify.}\\\\ &y=2\left(x-\frac{3}{2}\right)^2-1-\frac{9}{2}\\\\ &y=2\left(x-\frac{3}{2}\right)^2-\frac{2}{2}-\frac{9}{2}\\\\ &y=2\left(x-\frac{3}{2}\right)^2-\frac{11}{2}\\\\ \end{align*}
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