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: 33

Answer

The axis of symmetry is $x=-3.$ domain: $(-\infty,\infty)$ range: $[-6,\infty)$ .
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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. ------------------ $f(x)=x^{2}+6x+3$ $f(x)=(x^{2}+6x+9-9)+3$ $f(x)=(x+3)^{2}-6$ 1. opens up (a = $1 > 0$). 2. vertex: $(-3,-6). $The axis of symmetry is $x=-3.$ 3. x-intercepts: $(x+3)^{2}-6=0$ $(x+3)^{2}=6$ $x+3=\pm\sqrt{6}$ $x=-3\pm\sqrt{6}$ 4. y-intercept: $f(0)=(0)^{2}+6(0)+3=3$ The axis of symmetry is $x=-3.$ domain: $(-\infty,\infty)$ range: $[-6,\infty)$
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