Answer
$g(x)=-(x-2)^2+1=-x^{2}+4x-3$
Work Step by Step
We obtain $g(x)$ by reflecting $f(x)=x^2$ about the $x$-axis and shifting right 2 units and up 1 unit, i.e. $y=-f(x-2)+1$
$g(x)=-(x-2)^2+1=-(x^2-4x+4)+1=-x^{2}+4x-3$
College Algebra 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305115546
ISBN 13:
978-1-30511-554-5
Chapter 2, Functions - Section 2.6 - Transformations of Functions - 2.6 Exercises - Page 243: 68
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