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 740: 33


Please see image.

Work Step by Step

The graph of $f(x)=a(x-h)^{2}$ has the same shape as the graph of $y=ax^{2}.$ If $h$ is positive, the graph is shifted $h$ units to the right. If $h$ is negative, the graph is shifted $|h|$ units to the left. For $a\gt 0$, the parabola opens upward. For $a\lt 0$, the parabola opens downward. If $|a|$ is greater than 1, the parabola is narrower than $y=x^{2}.$ If $|a|$ is between $0$ and 1, the parabola is wider than $y=x^{2}.$ The vertex is $(h, 0)$, and the axis of symmetry is $x=h.$ --- $h=\displaystyle \frac{1}{2}$; shifted $0.5$ units to the right, $a=-3$; opens downward. The vertex is $(\displaystyle \frac{1}{2},0)$. The axis of symmetry is $x=\displaystyle \frac{1}{2}.$ Make a table of function values and plot the points, and join with a smooth curve.
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