(2010•丽水)△ABC中,∠A=∠B=30°,AB=2
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,把△ABC放在平面直角坐标系中,使AB的中点位于坐标原点O(如图),△ABC可以绕点O作任意角度的旋转.
(1)当点B在第一象限,纵坐标是
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时,求点B的横坐标;
(2)如果抛物线y=ax
2+bx+c(a≠0)的对称轴经过点C,请你探究:
①当a=
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,b=-
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,c=-
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时,A,B两点是否都在这条抛物线上?并说明理由;
②设b=-2am,是否存在这样的m的值,使A,B两点不可能同时在这条抛物线上?若存在,直接写出m的值;若不存在,请说明理由.
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