题目

已知：矩形纸片ABCD中，AB=26厘米，BC=18.5厘米，点E在AD上，且AE=6厘米，点P是AB边上一动点．按如下操作：步骤一，折叠纸片，使点P与点E重合，展开纸片得折痕MN（如图1所示）；步骤二，过点P作PT⊥AB，交MN所在的直线于点Q，连接QE（如图2所示）1.无论点P在AB边上任何位置，都有PQ_________QE（填“”、“”、“”号）；2.如图3所示，将纸片ABCD放在直角坐标系中，按上述步骤一、二进行操作：①当点P在A点时，PT与MN交于点Q1，Q1点的坐标是（_______，_________）；②当PA=6厘米时，PT与MN交于点Q2. Q2点的坐标是（_______，_________）；③当PA=12厘米时，在图3中画出MN,PT（不要求写画法），并求出MN与PT的交点Q3的坐标；3.点P在运动过程，PT与MN形成一系列的交点Q1，Q2，Q3……观察、猜想：众多的交点形成的图象是什么？并直接写出该图象的函数表达式．  答案： 1.2.；②．③画图见解析。3.抛物线 、函数关系式：解析:（1）．······························································································· 1分（2）①；②．······························································································· 3分③画图，如图所示．······································································································ 5分解：方法一：设与交于点．在中，，．，， ．又，．．．．················································································································ 7分方法二：过点作，垂足为，则四边形是矩形．，．设，则．在中，．．．．．（3）这些点形成的图象是一段抛物线．········································································ 8分函数关系式：．····································································· 10分说明：若考生的解答：图象是抛物线，函数关系式：均不扣分． 

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