How is the graph of #h(x)=6+2/3x^2# related to the graph of #f(x)=x^2#?

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Answer 1 · 2017-08-07T16:00:01

There is a stretch of #2/3# and a translation of #6#, both in the #y# direction

A translation of #a# in the #y-#direction tansforms the the function #f(x)# into

#y=f(x)+a#

A strech in the #y# direction is

#y=bf(x)#

The function is #f(x)=x^2# and the function after transformation is

#h(x)=2/3x^2+6#

The coefficients are

#b=2/3# for the stretch and

#a=6# for the translation graph{(y-x^2)(y-2/3x^2-6)=0 [-41.26, 40.97, -10.52, 30.6]}