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    26．如图所示.在平面直角坐标系中.矩形的边在轴的负半轴上.边在轴的正半轴上.且..矩形绕点按顺时针方向旋转后得到矩形．点的对应点为点.点的对应点为点.点的对应点为点.抛物线过点． (1)判断点是否在轴上.并说明理由, (2)求抛物线的函数表达式, (3)在轴的上方是否存在点.点.使以点为顶点的平行四边形的面积是矩形面积的2倍.且点在抛物线上.若存在.请求出点.点的坐标,若不存在.请说明理由． 解:(1)点在轴上················································· 1分 理由如下: 连接.如图所示.在中... . 由题意可知: 点在轴上.点在轴上．········································································· 3分 (2)过点作轴于点 . 在中.. 点在第一象限. 点的坐标为·························································································· 5分 由(1)知.点在轴的正半轴上 点的坐标为 点的坐标为···························································································· 6分 抛物线经过点. 由题意.将.代入中得 解得 所求抛物线表达式为:······················································· 9分 (3)存在符合条件的点.点．········································································· 10分 理由如下:矩形的面积 以为顶点的平行四边形面积为． 由题意可知为此平行四边形一边. 又 边上的高为2··································································································· 11分 依题意设点的坐标为 点在抛物线上 解得.. . 以为顶点的四边形是平行四边形. .. 当点的坐标为时. 点的坐标分别为., 当点的坐标为时. 点的坐标分别为.．··············································· 14分 【查看更多】

     

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