tg∠OCB=OB/OC=2，OB=4

OB = 4OA，OA= 1

A(- 1，0)，B(4，0)

( 1)

a=-0.5，b= 1.5

y=-0.5x^2+ 1.5x+2

(2)

k(AC)=2

k(k,2+ 1.5k-0.5k^2),0<； k≤4

kt:y-(2+ 1.5k-0.5k^2)=2(x-k)

y=0,T(0.25k^2+0.25k- 1,0)

BC:x+2y-4=0

k= 17/6，K()

s(max)=( 1/2)* 2√5 *(49/48)/√5 = 49/48

(3)

The condition of this problem is not enough, and the Q point must be on a parabola to get the solution.

k(BC)=-0.5

HG:y=-0.5x+m