College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.1 - Page 343: 26


The axis of symmetry is $x=$3. domain: $(-\infty,\infty)$ range: $(-\infty,1]$

Work Step by Step

To graph $f(x)=a(x-h)^{2}+k$, 1. Determine whether the parabola opens upward or downward. If $a>0$, it opens upward. If $a<0$, it opens downward. 2. Determine the vertex of the parabola. The vertex is $(h, k)$. 3. Find any x-intercepts by solving $f(x)=0$. The function's real zeros are the x-intercepts. 4. Find the y-intercept by computing $f(0)$. 5. Plot the intercepts, the vertex, and additional points as necessary Connect these points with a smooth curve that is shaped like a bowl or an inverted bowl. ------------------ $f(x)=1-(x-3)^{2}$ $f(x)=-(x-3)^{2}+1$ 1. opens down (a=$-1$). 2. vertex: (3, 1)$. $The axis of symmetry is $x=$3. 3. x-intercepts: $0=-(x-3)^{2}+1$ $(x-3)^{2}=1$ $x-3=\pm 1$ $x=3\pm 1$ $x=2$ or $x=4$ 4. y-intercept: $f(0)=-(0-3)^{2}+1=-8$ The axis of symmetry is $x=$3. domain: $(-\infty,\infty)$ range: $(-\infty,1]$
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