Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 3 - Quadratic Functions - Exercises for Skills for Completing the Square - Page 138: 20


$$ (\frac{1}{2},\frac{23}{4})$$

Work Step by Step

Completing the square in order to write the equation in the form $a(x-h)^2+k$, we find: $$5\left(x^2-x+\frac{7}{5}+\left(-\frac{1}{2}\right)^2-\left(-\frac{1}{2}\right)^2\right) \\ 5\left(\left(x-\frac{1}{2}\right)^2+\frac{7}{5}-\left(-\frac{1}{2}\right)^2\right) \\ 5\left(x-\frac{1}{2}\right)^2+\frac{23}{4}$$ The vertex is $(h,k)$, so we see that the vertex is: $$ (\frac{1}{2},\frac{23}{4})$$
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