题目

Mr. Baker has two children. One is a boy called Peter and the other is a daughter called Rose. Peter is an eleven-year-old boy. He studies at school. Rose is four and stays at home. One day, Mr. and Mrs. Baker went to their small shop and left their children at home. Peter had some homework to do. At five to nine he brought out his exercise-books. He began to do it in his father's study. About twenty minutes later his sister came in. She found a piece of paper and began to write something on it. What are you doing there, Rose? asked Peter. I'm writing a letter, answered the girl. “Oh? To who如图，已知抛物线经过原点O和x轴上另一点A，它的对称轴x=2与x轴交于点C，直线y=-2x-1经过抛物线上一点B（-2，m），且与y轴、直线x=2分别交于点D、E．（1）求m的值及该抛物线对应的函数关系式；（2）求证：①CB=CE；②D是BE的中点；（3）若P（x，y）是该抛物线上的一个动点，是否存在这样的点P，使得PB=PE？若存在，试求出所有符合条件的点P的坐标；若不存在，请说明理由．