Question

Using the graph of `f(x)=x^2` as a guide, describe the transformations, and then graph the function `g(x)=-2x^2`?

Answer 1

`f(x)=x^2`
`(x,y)`
graph{x^2 [-15, 15, -20, 20]}

`h(x)=color(red)(2)x^2`
Stretch by a vertical factor of `2`. (The graph rises faster and becomes skinnier.)
`(x,2y)`
graph{2x^2 [-15, 15, -20, 20]}

`g(x)=color(red)(-)2x^2`
Reflect the function across the `x`-axis.
`(x,-2y)`
graph{-2x^2 [-15, 15, -20, 20]}