题目内容
(本小题满分10分)已知
是二次函数,方程
有两个相等实根,且
.
(1)求
的解析式;
(2)求函数
与
所围成图形的面积.
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555507561.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555523516.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555601647.png)
(1)求
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555617447.png)
(2)求函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555507561.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555757613.png)
(1)
.
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232235559133180.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555897691.png)
(2)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232235559133180.png)
本试题主要是考查了二次函数的解析式的求解,以及二次函数的与平面图形的围成的曲边梯形面积的表示的综合运用。
(1)根据已知题意可知
,然后得到参数a,b,c的值
(2)根据已知条件,先求解交点坐标,然后运用定积分表示其面积的值。
解:(1)设
,则
.依题意有
,得
.∴
.
(2)由
或
,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232235559133180.png)
(1)根据已知题意可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232235561001109.png)
(2)根据已知条件,先求解交点坐标,然后运用定积分表示其面积的值。
解:(1)设
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223556116943.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223556131731.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232235561001109.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223556178613.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223555897691.png)
(2)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232235562091197.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823223556225365.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408232235559133180.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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