The graph of y=x^2 and y=cosx intercept in how many points?

They intercept in two points.

The graph y=x^2 is very basic so I suppose you know how it looks like.
It's like a U and starts from the origin (0,0)

The graph y=cosx is similar to y=x^2 but in a different way.
y=cosx doesn't pass from (0,0) it passes from (0,1) and then to (-1,0) and (1,0).
Basically, it goes like this..
~

If you know how the two graphs look like then you can understand why they intercept only two times.