－x²-3x+2
=-（x²+3x-2)
=-(x²+3x +9/4 -9/4 - 2)
=-[(x +3/2)²- 17/4]
=-(x +3/2)²+ 17/4
因为(x +3/2)²≥0,当x=-3/2时,取0
所以-(x +3/2)²≤0
所以
-(x +3/2)²+ 17/4≤17/4,当x=-3/2时,取最大值17/4