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.