f(x)=x^2-2x+3图象对称轴是x=1,
x=1时,f(x)取最小值f(1)=2,
x<1时,f(x)单调下降,f(0)=3,
x>1时,f(x)单调上升,f(2)=3,
所以,实数a取值范围是[1,2].