23.( 1 1) As shown in the figure, in the plane rectangular coordinate system, the three vertices of rectangular ABCD are known as B (4 4,0), C (8 8,0) and D (8 8,8). Parabola y=ax2+bx passes through point A and point C. 。

(1) Write the coordinates of point A directly and find the analytical formula of parabola;

(2) The moving point P starts from the point A and moves along the line AB to the end point B, while the point Q starts from the point C and moves along the line CD.

Move to the end D. The speed is 1 unit length per second, and the moving time is t seconds. Passing through point p is PE⊥AB, and AC is at point E.

① If you cross point E, do EF⊥AD at point F, and pass parabola at point G. When t is the value, what is the longest segment of eg?

② Connect EQ. During the movement of points P and Q, how many moments make △CEQ an isosceles triangle?

Please write the corresponding t value directly.

This is from 2009.

23.( 1 1) As shown in the figure, a parabola of a straight line x = passes through points A (6 6,0) and B (0 0,4).

(1) Find the parabolic analytical formula and vertex coordinates;

(2) Let point E (x, y) be the moving point on the parabola, which is located in the fourth quadrant. Quadrilateral OEAF is a parallelogram with OA as the diagonal. Find the functional relationship between the area s and x of parallelogram OEAF, and write the range of independent variable X;

① When the area of the parallelogram OEAF is 24, please judge whether the parallelogram OEAF is a diamond?

② Is there a point E that makes the parallelogram OEAF square? If it exists, find the coordinates of point e; If it does not exist, please explain why.

This is from 2007. If you want an answer, I'll give it to you next Monday. I'm a little busy today.