Let the exercise time be t (t > 0)
∴f(0)=c=0,|OP|=t
f(t)=t^2+bt=0==>; t(t+b)=0== >b=-t
∴f(x)=x^2-tx
(2) Analysis: ABCD is a rectangle, A( 1, 0), b (1, 5), D(4, 0).
∴C(4,-5)
parabola
Intersect with rectangular ABCD at m
The size of ∠AMP will not change when P moves.
Let x =1= = > f( 1)= 1-t
∴M( 1, 1-t)
∫P(t,0)
∴tan∠amp=( 1-t)/( 1-t)= 1
∴∠AMP=45
(3) analysis: ∵ rectangular ABCD,
A( 1,0)、B( 1,-5)、C(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.