Question

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

Answer 1

`h(x)` is `f(x)` scaled by `2/3` and shifted by 6 units negative ("down") on the `y`-axis

Explanation:

`f(x) =x^2`

`h(x) = 2/3* f(x) -6`

Hence: `h(x)` is `f(x)` scaled by `2/3` and shifted by 6 units negative ("down") on the `y`-axis. This can be shown by the graph of `h(x)` below.

graph{-6+2/3x^2 [-16.02, 16.01, -8.01, 8.01]}