Question

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

Answer 1

`y=-x^2+2` is `f(x)=x^2` reflected in the `x`-axis then shifted upward `2` units

Explanation:

If
`color(white)("xxx")g(x)=-f(x)=-x^2`
then every value of `g(x)` is the negative of a corresponding value of `f(x)`; that is `g(x)` is `f(x)` reflected in the `x`-axis.

If
`color(white)("xxx")y=g(x)+2`
then for each value of `x`
`color(white)("xxx")`the corresponding value of `y` is `2` greater than `g(x)`