Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - 3.1 - Quadratic Functions and Models - 3.1 Exercises - Page 249: 44



Work Step by Step

Vertex: $(h,k)=(\frac{5}{2},-\frac{3}{4})$ Standard form: $y=a(x−h)^2+k$ $y=a(x-\frac{5}{2})^2-\frac{3}{4}$ Now, use the point $(−2,4)$ to find $a$: $4=a(-2-\frac{5}{2})^2-\frac{3}{4}$ $4+\frac{3}{4}=a(-\frac{9}{2})^2$ $\frac{19}{4}=a(\frac{81}{4})$ $a=\frac{\frac{19}{4}}{\frac{81}{4}}=\frac{19}{4}\frac{4}{81}=\frac{19}{81}$ $y=\frac{19}{81}(x-\frac{5}{2})^2-\frac{3}{4}$
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