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: 37

Answer

(a) See graph, opens up, vertex $(-1,0)$, axis of symmetry $x=-1$, y-intercept $(0,1)$, x-intercept(s) $(-1,0)$. (b) domain $(-\infty,\infty)$, range $[0,\infty)$. (c) increasing on $(-1,\infty)$, decreasing on $(-\infty,-1)$.

Work Step by Step

(a) See graph for $y=x^2+2x+1=(x+1)^2+0$, we can find that the graph opens up, vertex $(-1,0)$, axis of symmetry $x=-1$, y-intercept $(0,1)$, x-intercept(s) $(-1,0)$. (b) We can determine the domain $(-\infty,\infty)$, range $[0,\infty)$. (c) The function is increasing on $(-1,\infty)$, decreasing on $(-\infty,-1)$.
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