题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193739-14456.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193739-67661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193739-75024.png)
(2)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-18260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-17134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-59044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-93393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-13664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-67385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-46911.png)
(3)是否存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-88638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193739-75024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-99024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-21905.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-74839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-99024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-76762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-20523.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-50394.png)
解析
试题分析:(1)∵f(-1)=0,∴a-b+c=0即b=a+c,故△=b2-4ac=(a+c)2-4ac=(a-c)2,
当a=c时,△=0,函数f(x)有一个零点;当a≠c时,△>0,函数f(x)有两个零点.
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-67385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-46911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-82282.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-29812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-81687.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-17134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-59044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-93393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-13664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-81687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-67385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-46911.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-67385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-46911.png)
(3)假设存在a,b,c满足题设,由条件①知抛物线的对称轴为x=-1且f(x)min=0;∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-54914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193741-42481.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193741-62062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-50394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193740-50394.png)
点评:本题考查函数零点个数与方程根的个数问题,以及存在性问题的处理方式,属于较难的题目.主要分析思路(1)通过对二次函数对应方程的判别式进行分析判断方程根的个数,从而得到零点的个数;(2)存在性问题的一般处理方法就是假设存在,然后根据题设条件求得参数的值.
核心考点
试题【已知二次函数(1)若试判断函数零点个数;(2)若对任意的,且<,(>0),试证明:>成立。(3)是否存在,使同时满足以下条件:①对任意,,且②对任意的,都有?若】;主要考察你对指数函数图象及性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193738-13851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-99122.png)
(Ⅰ)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-26998.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-49380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-26998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-43285.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-26998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-74857.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-65217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-23444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-23589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-61898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193736-45731.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193735-75497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193735-86220.png)
A.一个 | B.至少一个 | C.至多两个 | D.至多一个 |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-85244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-44820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-77772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-82263.png)
则称
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-21488.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-42506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-42506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193733-85244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193734-41772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193734-11063.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193734-94121.png)
是 .
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193726-43216.png)
(1)求实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193726-18624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193726-34168.png)
(2)证明
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193727-78708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193727-59415.png)
(3)已知
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193727-81539.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193728-19248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193728-28580.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819193728-77694.png)
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