已知二次函数
的图象是以原点为顶点且过点
的抛物线,反比例函数
的图象(双曲线)与直线
的两个交点间的距离为8,
.
(1)求函数
的表达式;
(2)当
时,讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f28af61b184c42164b8c1d9ebcb2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6b4195d2a7113b9707daa75a3c1cd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a301678a22fd9ebedb6c142a5a73bb4c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db36adca20dd88a44389304fc9074c2e.png)
更新时间:2020-02-18 16:52:18
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相似题推荐
解答题-问答题
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(0.4)
名校
解题方法
【推荐1】设为正数,函数
,满足
且
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294ed75f9d437ffc32235bcb602365c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b29189359ca2451f939ec5b54dfd399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6d11d3f6ea4e1342dd416f5adce409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10070e58dbfcc514e7d17dd8afc29f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
【推荐2】已知函数
的定义域为
,满足
.
(1)若
,求
的值;
(2)若
时,
.
①求
时
的表达式;
②若对任意
,都有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df0ddc9dc1d3928ad558669f792d16c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a709d20f9a223b729dbc4426fe0b774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9bf00816945629bfcde112091af785.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad5e3a4a816ab036fe3cee1ee7a4e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dee39c5a3e88d20afa8d372e187460d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71faf056756cabcfcdcc38d2a6dbdfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
【推荐3】某山区外围有两条相互垂直的直线型公路,为进一步改善山区的交通现状,计划修建一条连接两条公路和山区边界的直线型公路,记两条相互垂直的公路为
,山区边界曲线为C,计划修建的公路为l,如图所示,M,N为C的两个端点,测得点M到
的距离分别为2千米和5千米,点N到
的距离分别为4千米和2.5千米,以
在的直线分别为x,y轴,建立平面直角坐标系
,假设曲线C符合函数
(其中a,b为常数)模型.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/789ce56a-20db-4436-ace8-270dc579de58.png?resizew=172)
(1)求a,b的值;
(2)设公路l与曲线C相切于P点,P的横坐标为t.
①请写出公路l长度的函数解析式
,并写出其定义域;
②当t为何值时,公路l的长度最短?求出最短长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48580c1aaad3131fa92ebdb0aa2eed53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48580c1aaad3131fa92ebdb0aa2eed53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48580c1aaad3131fa92ebdb0aa2eed53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46532329c5aeb48626eac7929fdfaf81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277f46ca45508e520050e865d041a25c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/789ce56a-20db-4436-ace8-270dc579de58.png?resizew=172)
(1)求a,b的值;
(2)设公路l与曲线C相切于P点,P的横坐标为t.
①请写出公路l长度的函数解析式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2709ca478fb15ea08e8aa55328eae8e6.png)
②当t为何值时,公路l的长度最短?求出最短长度.
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解题方法
【推荐1】已知函数
.
(1)判断
的图象是否是中心对称图形?若是,求出对称中心;若不是,请说明理由;
(2)设
,试讨论
的零点个数情况.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7412310ce009d72857b1bd432fb568.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a3ccd295b61e3ccd31eca90ba713545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df49341b57eb107f416a014903ce25a8.png)
您最近一年使用:0次
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【推荐2】设函数
,
(1)当
时,求函数
在点
处的切线;
(2)若
,都有
,求正实数
的取值范围;
(3)当
时,曲线
上的点
处的切线与
相切,求满足条件的
的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e044c49cd2304f5057b85704e0901408.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefe012c95fa9c8bc294d25eb239a172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
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