Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Section 8.3 - Quadratic Functions and Their Graphs - Exercise Set - Page 626: 53

Answer

$f(x)=-3(x+2)^2+4$.

Work Step by Step

The given maximum value is $=4$ at $x=-2$. The vertex is $(h,k)=(-2,4)$ For the maximum value $a$ must be less than zero. Take the given function $g(x)=-3x^2$. The equation of the parabola that has the same shape is $\Rightarrow f(x)=-3(x-h)^2+k$ Substitute the values of $h$ and $k$. $\Rightarrow f(x)=-3(x-(-2))^2+4$. Simplify. $\Rightarrow f(x)=-3(x+2)^2+4$.
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