As shown in figure 15, in the plane rectangular coordinate system, point P starts from the origin O and moves right along the X axis for t (t(t>0) seconds at the speed of/kloc-0 per unit length per second. The parabola y = x2+bx+c passes through point O and point P. It is known that the three vertices of rectangular ABCD are A (1.

(1) Find c and b (expressed by algebraic expression with t);

(2) When 4 < t < 5, let a parabola intersect with line segments AB and CD at points M and N respectively.

① Do you think the size of ∠AMP will change during the movement of point P? If there are any changes, explain the reasons; If not, find the value of ∠AMP;

(2) Find the functional relationship between the area s of △MPN and t, and when finding the value of t, s =；;

(3) inside the rectangular ABCD (excluding the boundary), the points whose abscissa and ordinate are integers are called "good points". If the parabola divides these "good points" into two equal parts, please write the range of t directly.

Solution: Substitute (1) to get.

Then substitute it and you get, ∵, ∴.

(2) ① unchanged.

As shown in fig. 6, therefore, when.

∵ .∴

②

=

=

=

Solution =, get.

∵, ∴ Give up, ∴

⑶