(1) Find c and b (which can be expressed by algebraic expression with t);
(2) when t >; 1, the parABola intersects the line segment ab at point m, 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;
⑶ A point whose abscissa and ordinate are integers inside the rectangular ABCD (excluding the boundary) is called a "good point". If the parabola divides these "good points" into two equal parts, please write the range of t directly.
(1) Analysis: ∵ Point P starts from the origin O and moves to the right along the X axis, V= 1,
Let the exercise time be t.
∫ y = x 2+bx+c passes through point o (0,0) and point p (t,0).
∴ substitute x=t=0 into y = x 2+bx+c = > c = 0.
∴y=t^2+bt=0
∵t & gt； 0,∴b=-t
(2) Analysis: When t> 1, the parabola and the line segment AB intersect at point m.
∫ rectangular ABCD, A( 1, 0), B (1, 5), D(4, 0)
When x= 1, y =1-t.
∴M( 1, 1-t)
∵tan∠AMP = | PA |/| AM | = 1 = = & gt； ∠AMP=45
∴∠AMP is a constant value of 45.
(3) Analysis: ∵ rectangular ABCD, A( 1 0), B (1 5), C (4 4,5), d (4,0).
∴ The advantages of the rectangle are:
(2,- 1), (2,-2), (2,-3), (2,-4), (3,- 1), (3,-2), (3,-3), (3,-4)
The parabola divides these "advantages" into two equal parts.
When the parabola passes through (2, -3), (3,-1)
-3=2^2-2t==>； t = 7/2； - 1=3^2-3t==>； t= 10/3
When the parabola passes through (2, -4), (3, -2)
-4=2^2-2t==>； t = 4； -2=3^2-3t==>； t= 1 1/3
∫7/2 > 10/3，4 > 1 1/3
∴ take 7/2 < t <; 1 1/3
That is, when t is 7/2.