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 - 11.6 Quadratic Functions and Their Graphs - 11.6 Exercise Set - Page 741: 45

Answer

Please see image.
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Work Step by Step

The graph of $f(x)=a(x-h)^{2}+k$ has the same shape as the graph of $y=a(x-h)^{2}.$ If $k$ is positive, the graph of $y=a(x-h)^{2}$ is shifted $k$ units up. If $k$ is negative, the graph of $y=a(x-h)^{2}$ is shifted $|k|$ units down. The vertex is $(h, k)$, and the axis of symmetry is $x=h.$ For $a\gt 0$, the minimum function value is $k$. For $a\lt 0$, the maximum function value is $k.$ --- $k=4$; shifted $4$ units up. $h=2$ $a=-\displaystyle \frac{3}{2}$; opens downward The vertex is $(2,4)$. The axis of symmetry is $x=2.$ Since $a\lt 0$, the maximum function value is $4.$ Make a table of function values and plot the points, and join with a smooth curve.
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