how do you identify the graph of the function y=-(x-3)^2+2 ?

I would think of it as 

$$y-2 = -(x-3)^2$$

It has got a few extra numbers thrown in but it is a bit like      $$y=-x^2$$

This is a parabola.   It is concave down because of the - in front of the $$x^2$$

The vertex will be where y-2=0 and x-3=0

That is, the vertex will be (3,2)

I hope that helps. 

how do you identify the graph of the function y=-(x-3)^2+2 ?

This is a parabola that opens "downward" with its vertex at the point (3,2).