( 1998? Dalian) It is known that the quadratic function y=-x2+2x+3( 1) is transformed into the form of y=a(x-h)2+k by collocation method, and its function is pointed out.

Solution: (1) y =-x2+2x+3 =-(x2-2x)+3 =-(x-1) 2+4, that is, y=-(x- 1)2+4, and the symmetry axis of this parabola is x =.

(2) According to the analytical formula y=-x2+2x+3 of parabola, the opening direction of parabola is downward, and the intersection point with Y axis is (0,3).

∫y =-x2+2x+3 =-(x+ 1)(x-3)，

∴ The abscissas of the two intersections of parabola and X axis are-1 and 3, respectively.

From (1), we can also know that the symmetry axis of this parabola is x= 1, and the vertex coordinates are (1, 4);

So its image is as shown in the figure:

(3) According to the image, when y > 3, 0 < x < 2.