(1). (2分)试比较、的大小,并说明理由. (1),理由如下: 由折叠知: 在中,为斜边 故················································································································· 2分 (2). (1分)令,请问是否为定值?若是,请求出的值;若不是,请说明理由. 为定值.
···································································································· 3分 (3).在(2)的条件下,若为上一点且,抛物线经过、两点,请求出此抛物线的解析式. ,,
为等边三角形,················································································ 4分 作于. 的坐标为·································································· 5分 抛物线过点,, 所求抛物线解析式为········································································ 6分 (4).在(3)的条件下,若抛物线与线段交于点,试问在直线上是否存在点,使得以、、为顶点的三角形与相似?若存在,请求直线与轴的交点的坐标;若不存在,请说明理由. 由(3): 当时, ·························································· 7分
方法1:若与相似, 而.则分情况如下 时 为或····························· 8分 时 为或(0,1)······································ 9分 故直线与轴交点的坐标为或或或(0,1)··············· 10分 方法2:与相似时,由(3)得则或, 过点作垂直轴于则或 当时, 当 , ,…………………10分 |