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 344: 54


$ F(x)=-3(x-5)^{2}-7$

Work Step by Step

$ F(x)=a(x-h)^{2}+k, \quad$ where the vertex is $(h,k)$ has the same shape as $y=ax^{2}$, as the graph is obtained by translating (shifting left/right and up/down) To keep the same shape, a remains the same. The graph of F(x) is a parabola. If $a < 0,$ the parabola opens down, the vertex is its maximum point. If $a > 0$, the parabola opens up, the vertex is its minimum point. ----------------- To have the same shape as f(x) or g(x), a is either $-3$ or $3.$ Since our function has a maximum, its graph opens down, so $a=-3.$ The vertex$,\qquad (h,k)=(5,-7)$ so $ F(x)=a(x-h)^{2}+k$ $ F(x)=-3(x-5)^{2}-7$
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