题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-50742.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-35717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-65384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-35717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-42287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-29151.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-20964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-55186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-23446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-10460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-72261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071618-66153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-35717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-65384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071618-16134.png)
方程
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071618-13680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071618-13638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071619-10672.png)
∴该抛物线与
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071619-35559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071619-83665.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-35717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071619-39289.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
对于方程
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071619-11171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071620-29341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-29151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071620-55778.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071620-19216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071620-16324.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071620-82895.png)
此时抛物线为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071621-31232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071621-26376.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071621-53884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071618-13638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071621-21787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-10460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071622-45517.png)
由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-42287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071622-26330.png)
应有
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071622-62529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071622-71235.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071623-81715.png)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071620-19216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071623-81715.png)
(3)对于二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-50742.png)
由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-55186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071623-74242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-10460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071623-13522.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-20964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071623-10866.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071623-85207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071624-58708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071624-24312.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071624-85667.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071624-30969.png)
∵关于
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071625-80466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071625-91801.png)
∴抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-50742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
又该抛物线的对称轴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071625-34649.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-20964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071625-84105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071623-85207.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071625-92474.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071626-60209.png)
又由已知
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-55186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-23446.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-10460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071617-72261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071626-67770.png)
可知在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071618-66153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071615-35717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-65384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
(2)从当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071620-19216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071621-53884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-29151.png)
(3)通过关于
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071625-80466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071616-21712.png)
核心考点
试题【已知抛物线,(1)若,,求该抛物线与轴公共点的坐标;(2)若,且当时,抛物线与轴有且只有一个公共点,求的取值范围;(3)若,且时,对应的;时,对应的,试判断当时】;主要考察你对二次函数定义等知识点的理解。[详细]
举一反三
小题1:计算
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071606-81717.png)
小题2:画出函数y=-x2+1的图象
小题3:已知:如图,E,F分别是□ABCD的边AD,BC的中点.求证:AF=CE.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071606-33527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071555-76963.png)
小题1:求此抛物线的解析式
小题2:点P(x,y)为此抛物线上一动点,连接MP交此抛物线的对称轴于点D,当△DMN为直角三角形时,求点P的坐标;
小题3:设此抛物线与y轴交于点C,在此抛物线上是否存在点Q,使∠QMN=∠CNM ?若存在,求出点Q的坐标;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-21694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-54089.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-60151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-40787.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-34502.png)
(2)求证:无论
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-34502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-67870.png)
(3)已知抛物线与
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-67870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071547-21694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071535-45031.png)
(1)证明:不论k取何值,抛物线L的顶点C总在抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071535-52331.png)
(2)已知
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071535-29104.png)
(3)在(2)A、B间距取得最大值条件下(点A在点B的右侧),直线y=ax+b是经过点A,且与抛物线L相交于点D的直线. 问是否存在点D,使△ABD为等边三角形,如果存在,请写出此时直线AD的解析式;如果不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071520-25584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071520-67916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071521-11756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071521-82090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071521-45823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071521-91971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071521-97009.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071522-94527.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071522-20064.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071522-40330.jpg)
(1)写出点C的坐标;
(2)求出抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071520-67916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071522-67359.png)
(3)点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071522-32929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071523-78729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071522-32929.png)
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