(12分)如图,抛物线的顶点为 A (2,1),且经过原点 O ,与 x 轴的另一个交点为 B . 小题1:(1)求抛物线的解析式; 小题2:(2)在抛物线上求点 M ,使△ MOB 的面积是△ AOB 面积的3倍; 小题3:(3)连结 OA , AB ,在 x 轴下方的抛物线上是否存在点 N ,使△ OBN 与△ OAB 相似?若存在,求出 N 点的坐标;若不存在,说明理由.
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