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: 31

Answer

The axis of symmetry is $x=1$. domain: $(-\infty,\infty)$ range: $(-\infty, 4]$ .
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Work Step by Step

First, rewrite $f(x)=ax^{2}+bx+c$ in standard form, $f(x)=a(x-h)^{2}+k$ Graphing: 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. ------------------ $f(x)=2x-x^{2}+3$ $f(x)=-x^{2}+2x+3$ $f(x)=-(x^{2}-2x+1)+3+1$ $f(x)=-(x-1)^{2}+4$ 1. opens down (a = $-1 < 0$). 2. vertex: $(1, 4). $The axis of symmetry is $x=1.$ 3. x-intercepts: $-(x-1)^{2}+4=0$ $(x-1)^{2}=4$ $x-1=\pm 2$ $x=-1$ ,$\quad x=3$ 4. y-intercept: $f(0)=2(0)-(0)^{2}+3=3$ The axis of symmetry is $x=1$. domain: $(-\infty,\infty)$ range: $(-\infty, 4]$
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