抛物线y=x^2+(a+1)x+a-1的顶点的纵坐标的最大值是?

抛物线的对称轴为 x=-(a+1)/2
当x=-(a+1)/2 抛物线位于顶点
y=[-(a+1)/2]²-(a+1)²/2+a-1
=a-1-(a+1)²/4
=(1/4)[4a-4+(a+1)²]
=(1/4)(4a-4+a²+2a+1)
=(1/4)(a²+6a-3)
=(1/4)[(a+3)²-12]
=(1/4)(a+3)²-3
最大值为 -3