m为何值时,y=-x²+2x+m的函数值恒小于0

m为何值时,y=-x²+2x+m的函数值恒小于0
m为何值时,y=-x²+2x+m的函数值恒小于0

m为何值时,y=-x²+2x+m的函数值恒小于0
y=-x²+2x+m
=-(x²-2x+1)+1+m
=-(x-1)²+1+m
1+m＜0
m＜-1
m＜-1时,y=-x²+2x+m的函数值恒小于0

m<1

y=-x²+2x+m
y=-(x²-2x+1)+m-1
y=-(x-1)²+(m-1)
∵-(x-1)²≤0恒成立
∴m-1<0即m<1时y=-x²+2x+m的函数值恒小于0