This topic examines the synthesis of quadratic function, involving the coordinate characteristics of points on the coordinate axis, the vertex of parabola, the properties of rectangle, the analytical formula for finding straight lines by undetermined coefficient method, the properties of similar triangles, the increase and decrease of quadratic function, the classification idea and other knowledge points, which is comprehensive and difficult.

The first problem is to set x=0 to get the coordinates of point A, then get the coordinates of point B according to the ordinate of point A, and get the coordinates of C and D according to the properties of the vertex and rectangle of parabola.

Solution: (1) A (0,3), B (4,3), C(4,-1), D(0,-1).

(2) Let the analytical formula of straight line BD be y=kx+b(k is not equal to 0). Since the straight line BD passes through D(0,-1) and b (4,3), the detailed answer is here. /exercise/math/799838 As shown in figure 1, the edge AD of the rectangular ABCD is on the Y axis.

(2) If point P is a moving point on a parabola (point P does not coincide with points A and B), the parallel line L with point P as the y axis intersects with point G in line AB, and point H intersects with line BD, as shown in Figure 2.

① When the line segment PH=2GH, find the coordinates of point P;

② When point P is below straight line BD, point K is on straight line BD and satisfies △KPH∽△AEF, so as to find the maximum value of △KPH area.