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: 9


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, calcucate 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. $f(x)=x^{2}-2x+3 $ $ f(x)=(x^{2}-2x ) +3 \quad$... complete the square $f(x)=(x^{2}-2x+1-1)+3$ $f(x)=(x-1)^{2}+2$ b. vertex: $(h,k)=(1, 2)$, a=1, opens up, the vertex is a minimum y-intercept: f(0) = $3$ x-intercepts: f(x)=0 $(x-1)^{2}+2=0$ $(x-1)^{2}=-2$ (no x-intercepts, because a square can not be negative) c. see image (two pairs of additional points, either side of the vertex). d. domain: all reals, $\mathbb{R}$ range: $[2,\infty)$
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