Question

What is the graph of `y=sin^2 x`?

Answer 1

Here is the graph:
graph{(sinx)^2 [-10, 10, -5, 5]}

Recall the double-angle formula for cosine:
`cos(2x) = 1-2sin^2(x)`

Subtract `1` from both sides:
`cos(2x) -1 = -2sin^2(x)`

Divide both sides by `-2`
`-1/2cos(2x) + 1/2`

You now have a standard cosine equation with

Amplitude = `1/2`
Period = `pi`
Vertical Shift = up by `1/2`

Something important to recognize, if you compare this to the graph of `y=cos^2(x)`,(http://socratic.org/questions/what-is-the-graph-of-y-cos-2-x) you can see one is simply the negative of the other.