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【简答题】
如图,抛物线y=ax 2 +bx+2交x轴于A(﹣1,0),B(4,0)两点,交y轴C,与过点C且平行于x轴的直线交于另一点D,点P是抛物线上一动点. (1)求抛物线解析式及点D坐标; (2)点E在x轴上,若以A,E,D,P为顶点的四边形是平行四边形,求此时点P的坐标; (3)过点P作直线CD的垂线,垂足为Q,若将△CPQ沿CP翻折,点Q的对应点为Q′.是否存在点P,使Q′恰好落在x轴上?若存在,求出此时点P的坐标;若不存在,说明理由.
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