y=2x^2-4x+1
=2(x^2-2x+1-1)+1
=2[(x-1)^2-1]+1
=2(x-1)^2-1
对称轴是x=1,函数开口向上,则单调递增区间是:[1,+无穷),单调递减区间是(-无穷,1]