What is the transformations needed to obtain # f(x)= (x-2)^2# from the graph of #x^2#?

1 Answer
Alan N.
Sep 27, 2016

#x^2# shifted -2 units on the #x#-axis #=f(x)#

Explanation:

If #g(x)=x^2#and #f(x)=(x-2)^2#
then #f(x)=g(x-2)#

Hence the transformation needed to obtain #f(x)# from #g(x)# is a shift of -2 units on the #x#-axis.

This can be seen on the graphs of #g(x)# and f(x) below:

graph{x^2 [-5.69, 5.41, -1.44, 4.11]}

graph{(x+2)^2 [-5.69, 5.41, -1.44, 4.11]}

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