∵点P与点P'(1,3)关于x轴对称,∴P(1,-3),
故c=-3,
将点A(1-√3,0)代入抛物线y=a(x-1)²-3,
得a(1-√3-1)²-3=0,∴a=1,原抛物线的解析式是y=(x-1)²-3.