Question

How is the graph of `g(x)=-4x^2` related to the graph of `f(x)=x^2`?

Answer 1

See below

Explanation:

The graph of `f(x)=x^2` is the canonic parabola (see below)

graph{x^2 [-10, 10, -5, 5]}

If we multiply by `-1` the parabola change orientation with branches downwards as plotted below

graph{-x^2 [-10, 10, -5, 5]}

Now if we multiply by 4, branches of parabola trends to y axis (branches close) see below

graph{-4x^2 [-10, 10, -5, 5]}

Hope this helps