y=x²-(k+1)x+k-5
=x²-(k+1)x+【1/2(k+1)】²-【1/2(k+1)】²+k-5
=【x-1/2(k+1)】²-【1/2(k+1)】²+k-5
因为 对称轴是直线x=1
所以 1/2(k+1)=1
k=1