设k

/>设A(x1,0),B(x2,0)由题意得：|AB|=4|X2-X1|=4(x2-x1)^2=16x2^2-2x2x1+x1^2=16x1^2+2x1x2+x2^2-4x1x2=16(x1+x2)^2-4x1x2=16∵二次函数y=1/2x^2+kx+k-1/2的图象与x轴的两个交点A、B∴x1,x2为1/2x^2+kx+k-1/2=0的两个根△>0k^2-4/2*(k-1/2)>0k^2-2k+1>0(k-1)^2>0k≠1由韦达定理得：x1+x2=-2kx1x2=2(k-1/2)=2k-1代入(-2k)^2-4(2k-1)=164k^2-8k+4=16k^2-2k+1=4(k-1)^2=4k-1=±2k=3,-1∴y=1/2x^2+3x+5/2或y=1/2x^2-x-3/2