Y = 1/4x 2-x-8。

y(max)=(4ac-b^2)/4a=-9

According to the meaning of the question

Let BP pay AC to D.

Because S△BAD=S△BCD

So AD=CD

The d coordinate is (4, -4)

The vertex of the parabola is (m, -4).

The coordinates of point P are {(x, y)|x=2y-4} and y=-4}.

P(4，-4)

m=4