题目

People in the United States honor their parents with two special days: Mother’s Day, on the second Sunday in May, and Father’s Day, on the third Sunday in June. These days are set aside to show love and respect for parents. They raise their children and educate them to be responsible citizens. They give love and care. These two days offer a chance to think about the changing roles of mothers and fathers. More mothers now work outside the home. More fathers must help with child-care. These two special days are celebrated in many different ways. On Mother’s Day people wear carnations. A re如图1，在平面直角坐标系中，拋物线y=ax2+c与x轴正半轴交于点F(16，0)、与y轴正半轴交于点E(0，16)，边长为16的正方形ABCD的顶点D与原点O重合，顶点A与点E重合，顶点C与点F重合；    (1) 求拋物线的函数表达式； (2) 如图2，若正方形ABCD在平面内运动，并且边BC所在的直线始终与x轴垂直，抛物线始终与边AB交于点P且同时与边CD交于点Q(运动时，点P不与A、B两点重合，点Q不与C、D两点重合)。设点A的坐标为(m，n) (m>0)。 j 当PO=PF时，分别求出点P和点Q的坐标； k 在j的基础上，当正方形ABCD左右平移时，请直接写出m的取值范围； l 当n=7时，是否存在m的值使点P为AB边中点。若存在，请求出m的值；若不存在，请说明理由。