解:(1), ················································ 4分 (2)点,在抛物线上, ······················································ 2分
抛物线的解析式为 ······································ 1分 点坐标为
点在此抛物线上. ····························································· 1分 (3)假设存在这样的点,使得四边形的面积最大. 面积为定值, 要使四边形的面积最大,只需使的面积最大. 过点作轴分别交和轴于和,过点作轴交于.
设,
························································ 2分 ,有最大值. 当时,的最大值是,
四边形的面积的最大值为. ··································· 1分 此时点的坐标为. ·················································· 1分 所以存在这样的点,使得四边形的面积最大,其最大值为. |