College Algebra (6th Edition)

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

Chapter 3 - Summary, Review, and Test - Review Exercises - Page 435: 1


Axis of symmetry:$ x=-1$ Domain: $(-\infty,\infty)$ Range: $(-\infty,4)$

Work Step by Step

Follow the procedure on page 332, Graphing Quadratic Functions with Equations in Standard Form: 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. $a=-1$, so it opens downward. 2. Determine the vertex of the parabola. The vertex is $(h, k)=(-1,4)$. Axis of symmetry:$ x=-1$ 3. Find any x-intercepts by solving $f(x)=0$. $-(x+1)^{2}+4=0$ $(x+1)^{2}=4$ $x+1=\pm 2$ $x=-1\pm 2$ $x=-3$, or $x=1$ 4. Find the y-intercept by computing $f(0)$. $f(0)=-(0+1)^{2}+4=3$ 5. Plot the intercepts, the vertex, and additional points as necessary. Connect these points with a smooth curve. --------------------------------- Axis of symmetry:$ x=-1$ Domain: $(-\infty,\infty)$ Range: $(-\infty,4)$
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