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我们把一个半圆与抛物线的一部分合成的封闭图形称为“蛋圆”，如果一条直线与“蛋圆”只有一个交点，那么这条直线叫做“蛋圆”的切线．如图，点A、B、C、D分别是“蛋圆”与坐标轴的交点，已知点D的坐标为（0，-3），AB为半圆的直径，半圆圆心M的坐标为（1，0），半圆半径为2． （1）请你求出“蛋圆”抛物线部分的解析式，并写出自变量的取值范围； （2）开动脑筋想一想，相信你能求出经过点D的“蛋圆”切线的解析式． （3）如果直线x=m在线段OB上移动，交x轴D，交抛物线E，交BDF．连接DE和BE后，对于问题“是否存在这样的点E，使△BDE的面积最大？”小明同学认为：“当E为抛物线的顶点时，△BDE的面积最大．”他的观点是否 正确？提出你的见解，若△BDE的面积存在最大值，请求出m的值以及点E的坐标．
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