Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 252: 14


please see "step by step"

Work Step by Step

Rewrite f(x) in standard form, $f(x)=a(x-h)^{2}+k$, read the vertex, (h,x) For the y-intercept, calculate f(0) For the x- intercept, solve f(x) = 0 for x. If $a>0$, parabola opens up, the vertex is a minimum point, If $a<0$, parabola opens down, the vertex is a maximum. With this information (and possible additional points) sketch a graph Read the graph for range and domain. ------------------ a. factor out $-1$, $ f(x)=-(x^{2}-10x) \quad$... complete the square $f(x)=-(x^{2}-10x+5^{2}-5^{2})$ $f(x)=-(x-5)^{2}+25$ b. vertex: $(h,k)=(-1, -3)$, a=$-1$, opens down, the vertex is a maximum y-intercept: f(0) = $0$ x-intercepts: f(x)=0 -$x^{2}+10x=0$ $-x(x-10)=0$ x-intercepts: 0 and $10$. c. see image (one pair of additional points, either side of the vertex). d. domain: all reals, $\mathbb{R}$ range: $(-\infty,25]$
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