Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 3 - Linear and Quadratic Functions - 3.3 Quadratic Functions and Their Properties - 3.3 Assess Your Understanding - Page 146: 50

Answer

$f(x)=(x-2)^2+1$.

Work Step by Step

If the vertex of a graph is at $(h, k)$ then the general formula for the quadratic function is $f(x)=a(x-h)^2+k$. According to the picture the vertex of the graph is at $(2,1)$, hence the quadratic function becomes $f(x)=a(x-2)^2+1$. The point $(0,5)$ is on the graph, hence if we plug in the values we get: $5=a(0-2)^2+1\\ \\5=a(4)+1 \\5=4a+1\\ \\5-1=4a\\ 4=4a \\1=a$, Thus, the equation of the function is $f(x)=(x-2)^2+1$.
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