y=2(x-m/2)^2-m^2/2+2m^2-2.
y=(x-m/2)^2+(3m^2-4)/2.
则,二次函数的顶点为(m/2,(3m^2-4/2).
∵ 题设该顶点在y轴上,∴m/2=0
∴ m=0.