Question

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

Answer 1

`h(x)=2-x^2` is the graph of `f(x)=x^2` reflected in the X-axis and then shifted up `2` units.

Explanation:

If `f(x)=x^2`
then `g(x)=-x^2` is the reflection of `f(x)` in the X-axis
and
`h(x)=2-x^2` is (g(x)`shifted up`2# units