y=-(x²-mx)+2
=-(x²-mx+m²/4-m²/4)+2
=-(x²-mx+m²/4)+m²/4+2
=-(x-m/2)²+m²/4+2
所以最大值=m²/4+2=9/4
m²/4=1/4
m²=1
m=-1,m=1