题目
题型:北京模拟题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000201-39965.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000201-39509.gif)
(2)设这条抛物线与x轴的正半轴交于
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000201-36405.gif)
(3)设(2)中的抛物线与y轴交于点C,过A、B两点分别作两条直线与x轴垂直,又过点C作直线l,l与这两条直线依次交于x轴上方的E、F两点,如果梯形ABFE的面积等于9,求直线l的解析式。
(4)设线段AB上有一个动点P,P从A点出发向B点移动(但不与B重合),过P点作PM垂直x轴,交(2)中的抛物线于点M。设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000202-99697.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000202-47890.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000202-27480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000202-50982.gif)
∵无论m取什么实数,都有
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000203-36131.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000203-92973.gif)
∴方程
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000203-55125.gif)
(2)由题意,可设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000203-36556.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000204-37510.gif)
由一元二次方程根与系数关系,有
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000204-72644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000204-80144.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000204-61636.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000205-75692.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000205-86651.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000205-97832.gif)
∴所求抛物线的解析式为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000205-71459.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000205-48366.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000206-79479.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000206-32106.gif)
(3)∵抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000206-31586.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000207-25141.gif)
∴可设直线l的解析式为:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000207-79683.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000207-10599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000207-33452.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000208-75228.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000208-52866.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000208-61067.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000208-92574.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000209-82832.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000209-90576.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000209-28979.gif)
∴直线l的解析式为:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000210-82530.gif)
(4)存在t,使
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000210-38467.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000210-46460.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000211-33512.gif)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000211-64599.gif)
要使
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000211-39434.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000211-78637.gif)
<1>当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000211-91156.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000212-66945.gif)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000212-51281.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000212-71301.gif)
∵t=3时,点P与点B重合,不合题意,∴t≠3
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000212-28581.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000213-26974.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000213-57952.gif)
<2>当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000213-26413.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000213-88434.gif)
即有
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000214-96318.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000214-95893.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000214-20541.gif)
当t=0或t=3时均不符合题设条件,即这种情形不可能
综合<1><2>可知,存在t,当它的值为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000214-27905.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000215-21034.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020000215-90224.gif)
核心考点
试题【如图,已知抛物线(1)求证:无论m取什么实数,这条抛物线与x轴一定有交点。(2)设这条抛物线与x轴的正半轴交于两点(设A点在B点的左侧),当线段AB长为3时,求】;主要考察你对二次函数的图象等知识点的理解。[详细]
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