摘要：如图.抛物线经过的三个顶点.已知轴.点在轴上.点在轴上.且． (1)求抛物线的对称轴, (2)写出三点的坐标并求抛物线的解析式, (3)探究:若点是抛物线对称轴上且在轴下方的动点.是否存在是等腰三角形．若存在.求出所有符合条件的点坐标,不存在.请说明理由． 解:(1)抛物线的对称轴---2分 (2) ----5分 把点坐标代入中.解得---6分 ----------------7分 (3)存在符合条件的点共有3个．以下分三类情形探索． 设抛物线对称轴与轴交于.与交于． 过点作轴于.易得... ① 以为腰且顶角为角的有1个:． ······································································ 8分 在中. ································································································· 9分 ②以为腰且顶角为角的有1个:． 在中.···· 10分 ····························································································· 11分 ③以为底.顶角为角的有1个.即． 画的垂直平分线交抛物线对称轴于.此时平分线必过等腰的顶点． 过点作垂直轴.垂足为.显然． ． 于是······························································ 13分 ······································································································· 14分 注:第(3)小题中.只写出点的坐标.无任何说明者不得分．

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