Question

How is the graph of `y=-1/3x^2-4` related to the graph of `f(x)=x^2`?

Answer 1

See explanantion

Explanation:

`color(blue)(1->)`The general shape of the graph `y=x^2` is that of `uu`

`color(blue)(2->)`The -4 lowers the graph of `y=x^2` by 4

`color(blue)(3->)`Putting a minus sign in front of the `x^2` so that we have `y=-x^2-4` turns the whole thing upside. Now we have the general shape `nn`

`color(blue)(4->)`the `1/3` in `y=-1/3x-4` has the effect of widening the graph