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

Question

2175 views around the world

You can reuse this answer
Creative Commons License

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

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