Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.4 Properties of Quadratic Functions - 2.4 Assess Your Understanding - Page 158: 71


$a=6, b=0,c=2$

Work Step by Step

When the vertex of a graph is at $(h, k)$, then the general form for the quadratic function can be expressed as: $f(x) = a(x-h)^2+k~~~(1)$ We are given that the vertex is at $(h,k)=(0,2)$ Therefore, $f(x)= a(x-0)^2+k \implies f(x) =ax^2 +2 ~~~(2)$ Plug the point $(1,8)$ into equation (2) to obtain: $8 = a(1)^2+2 \implies a=6$ Thus, the equation of the function is: $f(x)=6x^2+2$ On comparing $f(x)=6x^2+2$ with $f(x) = ax^2+bx+c$, we get: $a=6, b=0,c=2$
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