∵f(1-x)=f（1+x）∴对称轴x=1∵与x轴两个交点之间距离为6∴x1=1-3=-2；x2=1+3=4∴f(x)=a(x+2)(x-4)=ax²-2ax-8a∵f(0)=4∴0-0-8a=4∴a=-1/2∴ f(x)=-1/2x²+x+4
