题目
题型:解答题难度:简单来源:不详
已知二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-50565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-95529.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-60743.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-27267.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-28745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-80507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-42600.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-42008.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-45504.png)
解析
试题分析:(Ⅰ)令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-62759.png)
得:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-19903.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060636-37237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060636-97305.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060636-44908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060636-68581.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-42008.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-28745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-80507.png)
即:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060637-24172.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060637-30838.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-28745.png)
∵开口方向向上,对称轴:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060637-46974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060637-12195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060634-28745.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060637-29892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060635-45504.png)
点评:二次函数在指定区间上的恒成立问题,可以利用韦达定理以及根的分布知识求解,属基础题
核心考点
试题【(本题满分12分)已知二次函数满足且.(Ⅰ)求的解析式; (Ⅱ)当时,不等式:恒成立,求实数的范围.】;主要考察你对一次函数的图象和性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060629-94454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060630-51172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060630-62880.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060630-60812.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060630-93238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060630-39242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060631-21361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060631-97970.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060627-94689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060617-78369.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060617-46377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060618-77004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060618-71565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060618-95837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060618-76525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060618-16700.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060618-20990.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060619-85764.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060619-85764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060619-42829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060619-88227.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060619-26180.png)
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