Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.4 Properties of Quadratic Functions - 2.4 Assess Your Understanding - Page 158: 65

Answer

(a) See graph (red curve). (b) domain $(-\infty,\infty)$, range $[\frac{7}{8},\infty)$. (c) decreasing on $(-\infty,-\frac{1}{4})$, increasing on $(-\frac{1}{4},\infty)$.

Work Step by Step

(a) To graph $y=2x^2+x+1=2(x+\frac{1}{4})^2+\frac{7}{8}$, start from $y=x^2$, shift the curve $\frac{1}{4}$ unit(s) to the left, stretch vertically by a factor of 2, then shift $\frac{7}{8}$ unit(s) up. See graph (red curve). (b) We can determine the domain $(-\infty,\infty)$, range $[\frac{7}{8},\infty)$. (c) The function is decreasing on $(-\infty,-\frac{1}{4})$, increasing on $(-\frac{1}{4},\infty)$.
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