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

Question

1540 views around the world

You can reuse this answer
Creative Commons License

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]}

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