题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-48108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-58077.jpg)
(1)求A,B,C三点的坐标;
(2)如果以A,P,Q三点构成的三角形与△AOC相似,求出点P的坐标;
(3)若将△APQ沿AP对折,点Q的对应点为点M. 是否存在点P,使得点M落在x轴上.若存在,求出点P的坐标;若不存在,请说明理由.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-15168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-78890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-68405.png)
解析
试题分析:(1)分别求得抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-48108.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-40695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-98819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-80413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-26373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-25319.png)
(3)构造正方形PQEF,ME=OA=4,AM=AQ=x,则PM=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-80413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-68088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-21485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-74421.png)
(1)在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-48108.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053900-63234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053900-82631.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053900-58805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053900-27658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053900-37132.png)
∴A(0,4),B(4,0),C(-1,0);
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-40695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-98819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-80413.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-26373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053901-67044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053901-40694.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053901-66099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-15168.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-25319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053901-40053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053902-16297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053857-78890.png)
(3)如图构造正方形PQEF,ME=OA=4,AM=AQ=x
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053902-20050.jpg)
PM=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-80413.png)
证得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-68088.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-21485.png)
有
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053902-88290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053902-81307.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053903-11146.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053903-29702.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053859-74421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053903-92017.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053903-14123.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053903-69567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053904-40126.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053858-68405.png)
点评:本题知识点多,综合性强,难度较大,一般是中考压轴题,主要考查学生对二次函数的熟练掌握情况.
核心考点
试题【已知抛物线交y轴于点A,交x轴于点B,C(点B在点C的右侧)。如图,过点A作垂直于y轴的直线l. 在y轴右侧、位于直线l下方的抛物线上任取一点P,过点P作直线P】;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
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053851-95500.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053851-45725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053846-94743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053846-80824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053846-49247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053846-25850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053846-58714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053847-32304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053847-78047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053847-93634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053847-91597.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053847-18971.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053847-29151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053829-63369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053830-71147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053830-66116.png)
(1)求y1与x的函数关系,并在图2中画出y1的图象;
(2)如图2,y2的图象是抛物线的一部分,其顶点坐标是(4,12),求点P的速度及AC的长;
(3)在图2中,点G是x轴正半轴上一点(0<OG<6),过G作EF垂直于x轴,分别交y1、y2于点E、F.
①说出线段EF的长在图1中所表示的实际意义;
②当0<x<6时,求线段EF长的最大值.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019053825-58283.png)
A.![]() | B.1 | C.![]() | D.2 |
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