Solve,

The analytical formula of parabola is y =-x-4;

(2) When point P moves to point (x, 0), there is BP2 = BD? BC,

Let x = 0, then y =-4,

The coordinates of point C are (0, -4).

∫PD∑AC，

∴△BPD∽△BAC，

∴.

BC =，

AB=6，BP=x-(-2)=x+2。

∴BD===.

∫BP2 = BD？ BC,

∴(x+2)2=，

The solution is X 1 =, X2 =-2 (-2 is irrelevant and omitted).

∴ The coordinate of point P is (,0), that is, when point P moves to (,0), BP2 = BD? BC;

(3)∫△BPD∽△BAC，

∴,

∴×

S△BPC=×(x+2)×4-

∵,

When x = 1, the maximum value of S△BPC is 3.

That is, when the coordinate of point P is (1, 0), the area of △PDC is the largest.