题目

如图（十五），抛物线（其中为正整数）与x轴相交于两个      不同的点A、B（点A位于点B的左侧），与y轴相交于点C，连结AC、BC． （1）求的值；（2分） （2）如图①，设点D是线段AC上的一动点，作DE⊥x轴于点F，交抛物线于点E，求 线段DE长度的最大值；（4分） （3）如图②，抛物线上是否存在点M，过点M作MN垂直x轴于点N，使得以点A、M、N为顶点的三角形与△ABC相似？若存在，求出点M的坐标；若不存在，请说明理由．（4分）    补全对话（本题共6小题，每小题1分，共6分）Grace: What did you do in class today, Sarah?Sarah: We had a 小题1:_________ about TV shows. My classmates like game shows and sports shows.Grace: Oh, I can’t小题2:________ them. But I love soap operas. I like to follow the story and see what小题3:_________ next.Sarah: Well, I don’t mind soap operas. But my favorite show is小题4:_______. Because I like to find out what is going on around the world.Grace: It’s boring.Sarah: Well, it may not be very exciting, but you can expect to learn a lot 小题5:_______ it, I hope to小题6:________ a reporter one day.