1 . 已知函数
的值域为
,且关于x的不等式
的解集为
.则有如下结论:
①
;
②函数
图像与直线
的两个交点之间的距离等于6;
③若关于x的不等式
的解集为
,则
;
④
的值与
的大小有关.
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63aaa178677e179fd17fb87877ccb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acd04f62bbce37e384254b337d24620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a2d1f0df2c0a8fae29b0117bdd7ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba18457e072ac06b381c3f73c90ba9b3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dd96cd4dd5d6d7dd660c00e443bbaa.png)
②函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/008e80e33ba7b182a6d82862fadc8009.png)
③若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585080b717e145c729881a42b4dd533b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88cadcbd692b0b44dac4bc2bf2bf2759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8503e2b6f81cb4c978a21a71ac5ef840.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
其中所有正确结论的序号是
您最近一年使用:0次
2 . 已知抛物线
与
轴交于
,
两点.
(1)求
的值和点
的坐标;
(2)在抛物线上任取一点
,作点
关于原点
的对称点
.
①是否存在
,
两点均在抛物线上的情况?如果存在,求
的长;如果不存在,请说明理由;
②请在网格中画出点
所在曲线的大致图像,并求当
取得最小值时点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb16dfd9f55e628ca27a1c49c12fff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/28/0b16460f-a2aa-4857-b1cd-e073bfbf77f5.png?resizew=152)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)在抛物线上任取一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
①是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
②请在网格中画出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42bda73a0934eb117ce945808ca7d44b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
3 . 设二次函数
,其图像过点
,且与直线
有交点.
(1)求证:
;
(2)若直线
与函数
的图像从左到右依次交于 A,B,C,D四点,若线段
能构成钝角三角形,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/225705de8bb0a3e08619e73c7f0c49be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af31a8d791f28399fc13be3250136dc.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1508daa783a4587860a1578e0bb332b.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af31a8d791f28399fc13be3250136dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd713a9809d5df1de33c6f11b81eca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b467455ea6b8b7f5e6dd53110bc22060.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
您最近一年使用:0次