y=x^2-2x-8=(x+2)(x-4)
所以A(-2,0)、B(4,0)、C(0,-8)
设P(x,y),则0
S四边形ABPC=S△AOC+S梯形OCPQ+S△PQB
=(1/2)|AO||CO|+(1/2)(|CO|+|PQ|)|OQ|+(1/2)|QB||PQ|
=(1/2)|AO||CO|+(1/2)|CO||OQ|+(1/2)|PQ||OQ|+(1/2)|QB||PQ|
=8+4x+(1/2)(-y)(x)+(1/2)(4-x)(-y)
=8+4x-2y
=8+4x-2(x^2-2x-8)
=-2x^2+8x+24
=-2(x^2-4x+4)+32
当x=2时,S有最大值32,这时P(2,8)