设抛物线y=x²-kx+k-1,根据条件,求k的值①抛物线的顶点在x轴上.②抛物线的顶点在y轴上.③抛物线经过原点④抛物线经过点(-1,-2)
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![设抛物线y=x²-kx+k-1,根据条件,求k的值①抛物线的顶点在x轴上.②抛物线的顶点在y轴上.③抛物线经过原点④抛物线经过点(-1,-2)](/uploads/image/z/3963594-66-4.jpg?t=%E8%AE%BE%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dx%26%23178%3B-kx%2Bk-1%2C%E6%A0%B9%E6%8D%AE%E6%9D%A1%E4%BB%B6%2C%E6%B1%82k%E7%9A%84%E5%80%BC%E2%91%A0%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E9%A1%B6%E7%82%B9%E5%9C%A8x%E8%BD%B4%E4%B8%8A.%E2%91%A1%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E9%A1%B6%E7%82%B9%E5%9C%A8y%E8%BD%B4%E4%B8%8A.%E2%91%A2%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%BB%8F%E8%BF%87%E5%8E%9F%E7%82%B9%E2%91%A3%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%BB%8F%E8%BF%87%E7%82%B9%EF%BC%88-1%2C-2%EF%BC%89)
设抛物线y=x²-kx+k-1,根据条件,求k的值①抛物线的顶点在x轴上.②抛物线的顶点在y轴上.③抛物线经过原点④抛物线经过点(-1,-2)
设抛物线y=x²-kx+k-1,根据条件,求k的值
①抛物线的顶点在x轴上.
②抛物线的顶点在y轴上.
③抛物线经过原点
④抛物线经过点(-1,-2)
设抛物线y=x²-kx+k-1,根据条件,求k的值①抛物线的顶点在x轴上.②抛物线的顶点在y轴上.③抛物线经过原点④抛物线经过点(-1,-2)
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