y=x²+2mx+3m
=x²+2·m·x+m²+3m-m²
=(x+m)²+3m-m²
所以顶点纵坐标为y=3m-m²=-(m-3/2)²+9/4≤9/4
所以顶点纵坐标的最大值为9/4,此时m=3/2