题文
如图所示,将矩形沿折叠,使点恰好落在上处,以为边作正方形,延长至,使,再以、为边作矩形. (1). (2分)试比较、的大小,并说明理由. 2)令,请问是否为定值?若是,请求出的值;若不是,请说明理由. 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. (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. |
题型:解答题 难度:中档
答案
(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 |
据专家权威分析,试题“如图所示,将矩形沿折叠,使点恰好落在上处,以为边作正方形,延..”主要考查你对 二次函数的定义,二次函数的图像,二次函数的最大值和最小值,求二次函数的解析式及二次函数的应用 等考点的理解。关于这些考点的“档案”如下:
二次函数的定义二次函数的图像二次函数的最大值和最小值求二次函数的解析式及二次函数的应用
考点名称:二次函数的定义 考点名称:二次函数的图像 考点名称:二次函数的最大值和最小值 考点名称:求二次函数的解析式及二次函数的应用
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