A(x-4)(x+2) crosses 0, -4, and a= 1/2.

y= 1/2x^2-x-4

2

BP/BD=BC/BP or BP/BC=BD/BP.

As long as the triangle BDP is similar to the triangle BCP

Triangle BDP is similar to triangle BCA.

As long as the triangle BCA is similar to the triangle BCP

BP/BC=BC/BA BP=20/6

P in 4/3, 0

three

DP parallel AC

Area of DPC =ABC-BDP-ACP=6*4/2-

Let DP=kAC

DPC area = ABC-k 2 ABC-ACP = 12- 12k 2-(6-6k)* 4/2 =- 12k 2+ 12k，0

There is a maximum value when k= 1/2.

P in 1, 0