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

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Answer 1 · 2018-08-14T11:06:30

See below

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