y=-1/2x^2+2x+1=-1/2(x^2-4x)+1 =-1/2(x^2-4x+4)+1+2 =-1/2(x-2)^2+3因为当x=2时有最大值y=3因为对称轴x=22-(-1)=34-2=2所以-1离对称轴最远,所以当x=-1时y=-1/2(-1-2)^2+3=-3/2所以值域是[-3/2,3]...