题目

China’s telecommunications supervisor has given long-awaited third-generation, or 3G mobile phone licenses(执照) to three mobile operators. The Ministry of Industry and Information Technology said China's biggest mobile operator, China Mobile, was given a license for TD-SCDMA, the domestically-developed 3G standard. k#    Wang Jianzhou, President of China Mobile said the company had already started construction of new networks to cover all cities by 2011. “After our testing operation of the network which started from last April, we have seen that the new technology has developed into （2007•玉溪）如图，已知二次函数图象的顶点坐标为C（1，0），直线y=x+m与该二次函数的图象交于A、B两点，其中A点的坐标为（3，4），B点在轴y上．（1）求m的值及这个二次函数的关系式；（2）P为线段AB上的一个动点（点P与A、B不重合），过P作x轴的垂线与这个二次函数的图象交于点E，设线段PE的长为h，点P的横坐标为x，求h与x之间的函数关系式，并写出自变量x的取值范围；（3）D为直线AB与这个二次函数图象对称轴的交点，在线段AB上是否存在一点P，使得四边形DCEP是平行四形？若存在，请求出此时P点的坐标；若不存在，请说明理由．