Question

抛物线y=a(x+3)(x-1)与X轴相交于A.B两点,点A在点B的右侧,过点A的直线交抛物线于另一点C,点C的坐标为（

Answer 1

(-2,6)代入y=a(x+3)(x-1)得a=-2

当CM⊥MP时,△CPM∽△APN,M1(0,6)

当CM⊥CA时,△MCP∽△ANP,AC:y=-2x+2,∴MC:y=0.5x+7

令0.5x+7=-2(x+3)(x-1)得x=-2或-1/4

∵Xc=-2∴Xm=-1/4

将Xm=-1/4代入y=-2(x+3)(x-1)得M2(-1/4,55/8)