y=1/4x²+1/2x+1
=1/4x²+1/2x+1/4+3/4
=(1/2x+1/2)²+3/4
(1/2x+1/2)²≥0
∴(1/2x+1/2)²+3/4≥3/4
∴值域是[3/4,+∞)