(1)AD=4,AB=2AD=8,AD=2AO=4,AO=2,OD=2√3D(0,2√3),C(4,2√3),A(-2,0)(2)y=ax^2+bx+c2√3=c2√3=16a+4b+c0=4a-2b+cc=2√34a+b=04a-2b+2√3=03b=2√3,b=2√3/3,a=-√3/6y=-x^2√3/6+2x√3/3+2√3=(-√3/6)(x^2-4x-12)=(-√3/6)[(x-2)^2-16]=(-√3/6)(x-2)^2+8√3/3对称轴L:x=2(3)B(6,0)设P(2,n)A)PD=PBP是BD垂直平分线与x=2的交点16+n^2=4+(n-2√3)^24n√3=4-16+12=0P1(2,0)B)PB=BDBD^2=12+36=16+n^2n^2=32,n=4√2和n=-4√2P2(2,4√2),P3(2,-4√2)C)PD=BD12+36=4+(n-2√3)^2(n-2√3)^2=44n=√44+2√3,和n=-√44+2√3所以,满足题意要求的点P共有5个