把y=x²-kx+k-1配方,配成頂點(diǎn)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
拋物線的頂點(diǎn)坐標(biāo)是[ k/2,(-k²+4k-4)/4 ]
①：當(dāng)拋物線的頂點(diǎn)在x軸上時(shí),頂點(diǎn)的縱坐標(biāo)值為0
(-k²+4k-4)/4=0
-k²+4k-4=0
k²-4k+4=0
(k-2)²=0
k-2=0
k=2
②：當(dāng)拋物線的頂點(diǎn)在y軸上時(shí),頂點(diǎn)的橫坐標(biāo)值為0
k/2=0
k=0
③：當(dāng)拋物線經(jīng)過原點(diǎn)(0,0)時(shí),把x=0,y=0代入y=x²-kx+k-1得
k-1=0
k=1
④：當(dāng)拋物線經(jīng)過點(diǎn)(-1,-2)時(shí),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