设f(x)=ax2+bx+c,f(0)=0,则c=0,
f(x+1)=ax2+(2a+b)x+a+b,
f(x)=ax2+bx,
f(x+1)-f(x)=2ax+a+b=2x,则
a=1,b=-1,即
f(x)=x2-x