5、2011中考压轴之四边形存在性问题 - 图文(2)

（3）在（2）中的直线AD交抛物线的对称轴于点M，抛物线上有一动点P，x轴上有一动点Q．是否存在以A、M、P、Q为顶点的平行四边形？如果存在，请直接写出点Q的坐标；如果不存在，请说明理由． 解：（1）根据题意，得

C y A O B x （第26题图）

C y D P1 Q1 O Q3 第26题图

Q4 B P4 x ?4a?2?c?0 ·············································· 1分 ??36a?6?c?0C P2 A 1??a??解得?·················································· 3分 4 ·

??c?31········· 4分 ?抛物线的解析式为y??x2?x?3 ·

4Q2 P3 顶点坐标是（2，4） ··············································································································· 5分

3) ·（2）D(4，························································································································· 6分

设直线AD的解析式为y?kx?b(k?0)

0)点D(4，3) ?直线经过点A(?2，、??2k?b?0 ······················································································································ 7分 ??4k?b?3?1?k????······························································································································· 8分 2 ·??b?1?y?1x?1 ·························································································································· 9分 2（3）存在． ·························································································································· 10分 ······················································································································ 11分 Q1(22?2，0) ··············································································································· 12分 Q2(?22?2，0) ·

······················································································································ 13分 Q3(6?26，0) ······················································································································ 14分 Q4(6?26，0)

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