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: 3

Answer

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

Work Step by Step

See page 335: Graphing Quadratic Functions with Equations in the Form $ f(\mathrm{x})=ax^{2}+bx+c.$ 1. Determine whether the parabola opens upward or downward. If $a>0$, it opens upward. If $a<0$, it opens downward. $a=-1$, opens downward. 2. Determine the vertex of the parabola. The vertex is $(-\displaystyle \frac{b}{2a}, f(-\frac{b}{2a}))$. $-\displaystyle \frac{b}{2a}=-\frac{2}{2(-1)}=1,\qquad f(1)=-1^{2}+2(1)+3=4$ Vertex: $(1,4).\quad $Axis of symmetry:$ x=1$ 3. Find any x-intercepts by solving $f(x)=0$. $-x^{2}+2x+3=0\quad/\times(-1)$ $x^{2}-2x-3=0$ $(x-3)(x+1)=0$ $x=-1$, or $x=3$ 4. Find the y-intercept by computing $f(0)$. Because $f(0)=c$ (the constant term in the function's equation), the y-intercept is $c$ and the parabola passes through $(0, c) = (0,3)$ 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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