Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 3 - Polynomial and Rational Functions - Chapter 3 Test Prep - Review Exercises - Page 397: 4

Answer

See graph, vertex $(0.5,2)$, axis $x=0.5$, no x-intercept, y-intercept $(0,3)$, domain $(-\infty,\infty)$, range $[2,\infty)$, increasing $(0.5,\infty)$, decreasing $(-\infty,0.5)$.

Work Step by Step

Step 1. Graph the function $f(x)=4x^2-4x+3=(2x-1)^2+2$ as shown in the figure. Step 2. We can identify the vertex $(0.5,2)$, axis $x=0.5$, Step 3. For x-intercepts, let $f(x)=0$, we have $(2x-1)^2+2=0$, no real solution thus no x-intercept. For y-intercept, we have $f(0)=3$ or $(0,3)$, Step 4. We can find domain $(-\infty,\infty)$, range $[2,\infty)$, and largest open intervals of the domain over which each function is increasing $(0.5,\infty)$, decreasing $(-\infty,0.5)$.
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