Is a (1, 0), b (1, 5), D (4 4, 0).
(1) Find c, 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 When finding the functional relationship between the area s of △MPN and t and finding the value of t;
(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.
Test center: Quadratic function synthesis problem.
Analysis: (1) parabola y=x2+bx+c passes through point o and point p, and the coordinates of point o and point p are substituted into the equation to get c and b;
(2)① When x= 1 and y= 1﹣t, if the coordinates of m are obtained, the number of times 𐃈 amp can be obtained.
② The quadratic function about t can be obtained by S=S quadrilateral AMNP-s △ PAM = s △ DPN+s trapezoid NDAM-s △ PAM, and the value of t can be obtained by the column equation;
(3) According to the graph, you can get the answer directly.
Solution: Solution: (1) Substitute x=0 and y=0 into y=x2+bx+c to get c=0.
Substitute x=t and y=0 into y=x2+bx to get t2+bt=0.
∫t > 0，
∴b=﹣t；
(2)① unchanged.
As shown in fig. 6, when x= 1 and y = 1-t, then M( 1, 1-t),
∫tan∠AMP = 1，
∴∠amp=45；
②S=S quadrilateral amnp-s △ PAM = s △ dpn+s trapezoid ndam-s △ PAM = (t-4) (4t-16)+[(4t-16)).
The solution t2-t+6 =,
Get: t 1=，t2=，
∫4 < t < 5，
∴t 1= Give up,
∴t=。
(3)