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

Published by Pearson

# Chapter 11 - Quadratic Functions and Equations - 11.6 Quadratic Functions and Their Graphs - 11.6 Exercise Set - Page 740: 29

#### Answer

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 of $y=ax^{2}$ is shifted $h$ units to the right. If $h$ is negative, the graph of $y=ax^{2}$ 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 $x=h.$ --- $h=1$; shifted $1$ unit to the right, $a=\displaystyle \frac{1}{2}$; opens upward. The vertex is $(1,0)$. The axis of symmetry is $x=1.$ Make a table of function values and plot the points, and join with a smooth curve.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.