题目
题型:不详难度:来源:
如图9,抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093901-79919.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093901-78219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093902-57958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093902-57797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093902-57958.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093902-57797.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093902-21408.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093902-66137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093903-31021.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093903-10310.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093903-71671.gif)
(1)(3分)求线段
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093903-58269.gif)
(2)(3分)求该抛物线的函数关系式.
(3)(4分)在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093901-78219.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-24743.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-33694.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-24743.gif)
答案
(1)2
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
(2)y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-62497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-59180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
(3)(0,0),(6-2
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-48305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-41453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-14349.gif)
即:OA=2,OB=6 ……1分
∵△OCA∽△OBC
∴OC
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
∴OC=2
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
∴线段OC的长为2
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
(2)解:∵△OCA∽△OBC
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093906-86496.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093906-24032.gif)
设AC=k,则BC=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
由AC
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
k
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
解得k=2(-2舍去)
∴AC=2,BC=2
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
过点C作CD⊥AB于点D
∴OD=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093906-22931.gif)
∴CD=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093906-41818.gif)
∴C的坐标为(3,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
将C点的坐标代入抛物线的解析式得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
∴a=-
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-62497.gif)
∴抛物线的函数关系式为:
y=-
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-62497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-74006.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-59180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
(3)解:①当P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-41453.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-41453.gif)
∴P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-41453.gif)
②当P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-14349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-14349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-14349.gif)
∴P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-14349.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
③当P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-94288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-94288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-94288.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-94288.gif)
∴P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-94288.gif)
④
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093905-48305.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-22672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-22672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-22672.gif)
∴P
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093907-22672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
∴在x轴上存在点P,使△BCP为等腰三角形,符合条件的点P的坐标为:
(0,0),(6-2
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093904-97162.gif)
核心考点
试题【如图9,抛物线与轴交于、两点(点在点的左侧),抛物线上另有一点在第一象限,满足∠为直角,且恰使△∽△.(1)(3分)求线段的长. (2)(3分)求该抛物线的函数】;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/20191019/20191019093856-53623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093857-43094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093857-43094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093848-29871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093849-81583.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093849-25276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093849-84635.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093849-68335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093850-92050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093850-74733.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093850-32301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093850-83093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093850-24830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093848-29871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093851-58755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093851-37231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093851-38590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093851-88297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093851-58755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093851-37231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093851-88297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093852-78386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093840-58850.jpg)
(1)直接写出点A的坐标,并求出抛物线的解析式;
(2)动点P从点A出发.沿线段AB向终点B运动,同时点Q从点C出发,沿线段CD
向终点D运动.速度均为每秒1个单位长度,运动时间为t秒.过点P作PE⊥AB交AC于E
①过点E作EF⊥AD于点F,交抛物线于点G.当t为何值时,线段EG最长?
②连接EQ.在点P、Q运动的过程中,判断有几个时刻使得△CEQ是等腰三角形?
请直接写出相应的t值.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019093835-38589.png)
![]() | … | ![]() | ![]() | 0 | 1 | 2 | … |
![]() | … | 11 | 2 | -1 | 2 | 5 | … |
A.y=x2+3 | B.y=x2-3 | C.y=(x+3)2 | D.y=(x-3)2 |
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