题干

如图(1),直线y=﹣x+3与x轴、y轴分别交于点B、点C,经过B、C两点的抛物线y=x2+bx+c与x轴的另一个交点为A,顶点为P.

(1)求该抛物线的解析式;

(2)在该抛物线的对称轴上是否存在点M,使以C、P、M为顶点的三角形为等腰三角形?若存在,请直接写出所有符合条件的点M的坐标;若不存在,请说明理由;

(3)连接AC,在x轴上是否存在点Q,使以P、B、Q为顶点的三角形与△ABC相似?若存在,请求出点Q的坐标;若不存在,请说明理由;

(4)当0<x<3时,在抛物线上求一点E,使△CBE的面积有最大值.

(图(2)、图(3)供画图探究)

上一题 下一题 0.0难度 选择题 更新时间:2015-03-10 06:53:41

答案(点此获取答案解析)

解:(1)由已知,得B(3,0),C(0,3),

3=c0=9+3b+

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阅读理解

    The advice offered from any other 82-year-olds might have made young people yawn and roll their eyes. But when former South African president Nelson Mandela advised two dozen local youth leaders in Los Angeles to take education seriously, his audience was listening.

    The famed old man said to the young people that if they expected to improve the lives of others in the future, they must work at improving their own lives now. "Education is one of the most important weapons you have,” Mandela advised. “It will place you in a far better position to serve yourself and your community.”

     “The point is, he was young once and rebellious(叛逆的)once and he kept his dream alive, just as you each have dreams,” explained South Africa’s ambassador to the United States, Sheila Sisulu, as she introduced Mandela to the young crowd.

    Asked for specific advice about changing society by 21-year-old Ahmed Younis, Mandela suggested that somehow helping arouse more American interest in foreign affairs might be a start.

    There is an impression that Americans, in general, have not followed international developments properly, Mandela said. “I’m not making that statement myself, but there are serious political analysts who say Americans are not well informed as to what has happened in the world.”

    22-year-old Omari Trice said Mandela left him full of enthusiasm. “ He’s a person who set the tone for an entire nation, said Trice. “You come away feeling you need to be a superman in order to get things done.”