题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071650-73844.png)
小题1:求抛物线的解析式;
小题2:将△OAC绕x轴旋转一周,求所得旋转体的表面积;
小题3:如图2,将△OAC沿x轴翻折后得△ODC,设垂直于x轴的直线l:x=n与(1)中所求的抛物线交于点M,与CD交于点N,若直线l 沿x轴方向左右平移,且交点M始终位于抛物线上A、C两点之间时,试探究:当n为何值时,四边形AMCN的面积取得最大值,并求出这个最大值.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071650-31829.png)
答案
小题1:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071650-10278.png)
小题2:在图1中作AH
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071651-87015.png)
则OH=4, ------------------6分
当x=4时,y="2" 所经A(4,2),OA=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071651-71693.png)
表面积=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071651-89572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071651-40494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071652-22404.png)
小题3:连接AD,交OC于E,----------------------------------9分
则OE=4,BE=OE-OB=1,EC=4
利用三角形相似(略)可得AE=2,所以DE=2, D(4,-2)
由C(8,0)、D(4,-2)得直线CD解析式
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071652-48429.png)
得N(n,0.5n-4)
由抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071650-10278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071652-42140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071652-26297.png)
所以MN=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071652-54546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071653-31179.png)
四边形AMCN的面积=0.5MN×CE=0.5×(
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071653-31179.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071653-73321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071653-78068.png)
所以,当n=5时,四边形AMCN的面积取得最大值,这个最大值是9. -------12分
解析
(2)先用勾股定理求出OA长,然后利用表面积公式求解;
(3)先求出四边形面积的表达式,然后根据一元二次函数的性质求出面积最大值
核心考点
试题【如图1,抛物线与x轴交于B(3,0) 、C(8.0)两点,抛物线另有一点A在第一象限内,连接AO、AC,且AO=AC.小题1:求抛物线的解析式;小题2:将△OA】;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/20191019/20191019071645-25273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071645-65055.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071635-99756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071635-27328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071635-25652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071635-73139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-97883.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-40232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-10076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-40232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-10076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071635-73139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-17490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-86282.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071637-70215.png)
(1)求此抛物线的解析式;
(2)过点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-40232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071637-32010.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071637-96842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-10076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071637-60039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071638-55579.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-10076.png)
(3)已知点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071638-84830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071635-73139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071636-10076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071638-84830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071635-25652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071638-24119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071638-10850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071638-84830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071638-76673.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071639-67012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071631-34892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019071631-31249.png)
![](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)
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)
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