+118723 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. 
+130511 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).
+118723 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.
