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/20190819/20190819060858-33631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-18126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-97887.png)
解集为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-52072.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-24371.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-64382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060900-52352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060900-19205.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060900-37222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060900-78282.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060900-92023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060901-33629.png)
解析
试题分析:(1)∵
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-18126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060901-55390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060901-20601.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-97887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060901-90213.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060859-52072.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060901-49054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060902-25640.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060902-80471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060902-97176.png)
由①②③得:a=2,b=1,c=-3
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060900-92023.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060902-80493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060903-79417.png)
①若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060903-36544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060903-25640.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060903-35920.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060903-49035.png)
②若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060903-94627.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060904-63251.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060904-74627.png)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060901-33629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060904-38600.png)
③若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060904-26532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060905-72670.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060905-62232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060905-34658.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060901-33629.png)
点评:本题第二问需讨论抛物线对称轴与给定区间的关系,从而确定最值点的位置,对学生有一定的难度
核心考点
试题【(满分12分)已知二次函数满足:,且的解集为(1)求的解析式;(2)设,若在上的最小值为-4,求的值.】;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/20190819/20190819060854-22319.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060854-37860.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060852-17315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060852-18050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060852-37734.png)
① 已知不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060848-21819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060849-11927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060849-37779.png)
② 若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060849-65297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060849-91907.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060849-74947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060847-55242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060847-83900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819060847-62594.jpg)
A.{2} | B.(-∞,2] | C.[2,+∞) | D.(-∞,1] |
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