把y=x²-kx+k-1配方,配成顶点式
y=x²-kx+k-1
=(x²-kx)+k-1
=[x²-kx+(k/2)²]-(k/2)²+k-1
=(x-k/2)²+(-k²+4k-4)/4
抛物线的顶点坐标是[ k/2,(-k²+4k-4)/4 ]
①：当抛物线的顶点在x轴上时,顶点的纵坐标值为0
(-k²+4k-4)/4=0
-k²+4k-4=0
k²-4k+4=0
(k-2)²=0
k-2=0
k=2
②：当抛物线的顶点在y轴上时,顶点的横坐标值为0
k/2=0
k=0
③：当抛物线经过原点(0,0)时,把x=0,y=0代入y=x²-kx+k-1得
k-1=0
k=1
④：当抛物线经过点(-1,-2)时,把x=-1,y=-2代入y=x²-kx+k-1得
(-1)²-k×(-1)+k-1=-2
1+k+k-1=-2
2k=-2
k=-1