Solution: The analytical formula of the solution: (1)∫ translation quadratic function is y=2(x- 1)2.

The symmetry axis of the translated quadratic function is x= 1, and the coordinate of point A is (0,2).

(2) The symmetry axis of the translation quadratic function is x= 1,

∴ The coordinate of the intersection point b of the function y=2x2 is (1, 2),

∫ y = 2 (x-1) The coordinate of vertex d of 2 is (1,0).

The quadrilateral OABD is a rectangle.

(3) When the point P is at P 1, △DBP is a right triangle with the line segment DB on the right.

At this time, the coordinate of point P is (0,0),

When the point P is at P2, △DBP is a right triangle with the right side of the line segment DB.

At this time, the coordinate of point P is (-1, 2).