函数y=-x²+4x与x轴交于点O,A,点O为坐标原点,点F为该抛物线上的点,点E为抛物线对称轴上的点且以A,O,F,E四点为顶点的四边形为平行四边形,求F的坐标
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![函数y=-x²+4x与x轴交于点O,A,点O为坐标原点,点F为该抛物线上的点,点E为抛物线对称轴上的点且以A,O,F,E四点为顶点的四边形为平行四边形,求F的坐标](/uploads/image/z/1612658-2-8.jpg?t=%E5%87%BD%E6%95%B0y%3D-x%26%23178%3B%2B4x%E4%B8%8Ex%E8%BD%B4%E4%BA%A4%E4%BA%8E%E7%82%B9O%2CA%2C%E7%82%B9O%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%2C%E7%82%B9F%E4%B8%BA%E8%AF%A5%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8A%E7%9A%84%E7%82%B9%2C%E7%82%B9E%E4%B8%BA%E6%8A%9B%E7%89%A9%E7%BA%BF%E5%AF%B9%E7%A7%B0%E8%BD%B4%E4%B8%8A%E7%9A%84%E7%82%B9%E4%B8%94%E4%BB%A5A%2CO%2CF%2CE%E5%9B%9B%E7%82%B9%E4%B8%BA%E9%A1%B6%E7%82%B9%E7%9A%84%E5%9B%9B%E8%BE%B9%E5%BD%A2%E4%B8%BA%E5%B9%B3%E8%A1%8C%E5%9B%9B%E8%BE%B9%E5%BD%A2%2C%E6%B1%82F%E7%9A%84%E5%9D%90%E6%A0%87)
函数y=-x²+4x与x轴交于点O,A,点O为坐标原点,点F为该抛物线上的点,点E为抛物线对称轴上的点且以A,O,F,E四点为顶点的四边形为平行四边形,求F的坐标
函数y=-x²+4x与x轴交于点O,A,点O为坐标原点,点F为该抛物线上的点,点E为抛物线对称轴上的点
且以A,O,F,E四点为顶点的四边形为平行四边形,求F的坐标
函数y=-x²+4x与x轴交于点O,A,点O为坐标原点,点F为该抛物线上的点,点E为抛物线对称轴上的点且以A,O,F,E四点为顶点的四边形为平行四边形,求F的坐标
y=-(x-2)^2+4,
A(4,0),对称轴x=2,
设F为(x,y),
AOFE是平行四边形,则E(2,y),
|EF|=4,
|x-2|=4,x=6,或x=-2,
y=-12,或y=-12,
F(6,-12)或(-2,-12).
A(4,0)
O(0,0)
E(2,-4)
F(2,4)
Y=-X²+4X=-(X-2)²+4,
顶点(2,4),
∴E(2,4),
∴F(2,-4)。
①AO=4为平行四边形的边→FE∥AO且FE=4→F(-2,-12)或F(6,-12)
②AO为平行四边形的对角线→F(2,-4)