Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - Review Exercises: Chapter 11 - Page 773: 34

Answer

The graph is shown below,

Work Step by Step

The coefficient of ${{x}^{2}}$ is not 1. Factor out 2 from the first two terms. Therefore, $f\left( x \right)=2\left( {{x}^{2}}-6x \right)+23$ Complete the square by taking half the coefficient of $x$, squaring it, and subtracting it inside the parentheses. $\begin{align} & f\left( x \right)=2\left( {{x}^{2}}-6x+9-9 \right)+23 \\ & =2\left( {{x}^{2}}-6x+9 \right)-\left( 2\cdot 9 \right)+23 \\ & =2\left( {{x}^{2}}-6x+9 \right)-18+23 \\ & =2{{\left( x-3 \right)}^{2}}+5 \end{align}$ Choose some $x$ values, and compute the respective $y$ values. $x$, $f\left( x \right)=2{{\left( x-3 \right)}^{2}}+5$ $1$, $13$ $2$, $7$ $3$, $5$ $4$, $7$ $5$, $13$ Plot the above points and draw a smooth curve through the points.
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