名校
1 . 在平面直角坐标系
中,抛物线
与
轴交于点
,抛物线
的顶点为
,直线
.
(1)当
时,画出直线
和抛物线
,并直接写出直线
被抛物线
截得的线段长;
(2)随着
取值的变化,判断点
,
是否都在直线
上并说明理由;
(3)若直线
被抛物线
截得的线段长不小于2,结合函数的图象,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d2292b9b81580718770d52fa7d9670e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1de14c98dff0e1fb25a27c92e3f35a0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/1d269f71-365e-45f4-9193-fb01e02f6f94.png?resizew=203)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)随着
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
2 . 已知函数
.
(1)若
在区间
上的最小值为
,求
的值;
(2)若存在实数
,
使得
在区间
上单调且值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e070b78d34f676862357a6e8140db2fa.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2019-07-09更新
|
2466次组卷
|
8卷引用:浙江省杭州市2018-2019学年高一第二学期期末数学试题
名校
3 . 已知函数
的图象上有两点
,
.函数
满足
,且
.
(1)求证:
;
(2)求证:
;
(3)能否保证
和
中至少有一个为正数?请证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4753463638237ed69779fff0c66746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2d666c964eaf1879e069d971b0d636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431521d6928b08a6d75e17676219dd64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/196be101149acfb6a6c4ceca7fc96828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5089dc8320c35b7068b66001e2b69f8.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe716b3a010661bc2ffd99a6263c5108.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90e8d5d7fed033f48270b1ff825fcd5.png)
(3)能否保证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6ae35ea314b3b3c56dc3500e14aa8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d145687ec9531a97ab689a0a17023f.png)
您最近一年使用:0次
4 . 如图,已知抛物线
的图象经过点
,与
轴交于点
,抛物线的顶点为
,对称轴与
轴相交于点
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/2ba7a91d-6013-425a-bc10-9b67d02dd0df.png?resizew=125)
(1)求抛物线的解析式.
(2)若点
在直线
上,当
时,求点
的坐标.
(3)在(2)的条件下,作
轴于
,点
为
轴上一动点,
为直线
上一动点,
为抛物线上一动点,当以点
四点为顶点的四边形为正方形时,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e59da5115d0dafea24822245f92c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acab25020a238f64d2b363615d105b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/2ba7a91d-6013-425a-bc10-9b67d02dd0df.png?resizew=125)
(1)求抛物线的解析式.
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fcf0b08d002a21f5494032cf0d15440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)在(2)的条件下,作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b1da9046b4cb82135a4a1eaa528c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8c0634801d7dd15d3880d0c3f90d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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5 . 已知函数
.
(1)若
,求实数
的取值范围;
(2)设
的极大值为
,极小值为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ae9c590045b246110a80573c361ff3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8a0f86edc5e8136f988bbebb4c5334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57584805a70c17d752bbd0def995accc.png)
您最近一年使用:0次
2019-04-29更新
|
1100次组卷
|
5卷引用:【校级联考】河北省示范性高中2019届高三下学期4月联考数学(文)试题
名校
6 . 已知函数
,其中
为实数.
(Ⅰ)当
时,求函数
的最小值;
(Ⅱ)若
在
上为增函数,求实数
的取值范围;
(Ⅲ)对于给定的负数
,若存在两个不相等的实数
(
且
)使得
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8150bd4825bd86621322e07f5c4bf77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅲ)对于给定的负数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1b87613e5700880384c5a3e3112c2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2037b0bad7c7a312bac1ac0653d9a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0787d6cb7fde5e0490ebf1d62b4ad6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45bcd8f6ede8cc2513ad41402f40086.png)
您最近一年使用:0次
2019-07-09更新
|
708次组卷
|
6卷引用:浙江省宁波市镇海区镇海中学2018-2019学年高一上学期期中数学试题
名校
解题方法
7 . 已知函数
,其最小值为
.
求
的表达式;
当
时,是否存在
,使关于t的不等式
有且仅有一个正整数解,若存在,求实数k的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb555e8a3da52f7e97e65fef75f22c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5448a4a8eb2fb6c5d87695bb70b9f433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5448a4a8eb2fb6c5d87695bb70b9f433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ee03c46c16b7307057e0a25e78192d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bb0bb8bce4183a5f083e0db361f4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074ffc3132fa78bbe00afe2f189a06e6.png)
您最近一年使用:0次
2019-03-08更新
|
1116次组卷
|
4卷引用:【校级联考】广东省肇庆联盟校2018-2019学年高一上学期期末考试数学试题
10-11高三上·四川成都·阶段练习
8 . 已知函数
.给出下列命题:①
必是偶函数;②当
时,
的图像必关于直线x=1对称;③若
,则
在区间
上是增函数;④
有最大值
. 其中正确的序号是 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1124bdfc04fe6e296c39da7ee4c5640.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90273593dca08da1b9e33e3a8663c514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8e281e0aebdba052969bf11cf86430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/2010/9/23/1569838391599104/1569838396899328/STEM/ba691d1458bb44de872b0f4f4d5697fa.png?resizew=52)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/328622db9462229e5104c43f125a67d4.png)
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2019-01-30更新
|
1506次组卷
|
5卷引用:成都市玉林中学2010—2011学年度(上学期)诊断性评价模拟试卷(理科)
(已下线)成都市玉林中学2010—2011学年度(上学期)诊断性评价模拟试卷(理科)(已下线)2012-2013学年山西省忻州一中高一上学期期末数学试卷人教A版(2019) 必修第一册 突围者 第三章 模拟高考(已下线)人教B版2019必修第一册综合测试(基础过关)-2020-2021学年高一数学单元测试定心卷(人教B版2019必修第一册)新疆维吾尔自治区和田地区墨玉县2023届高三上学期期中教学情况调研数学(文)试题
9 . 定义在
上的函数
,对任意的
都有
且当
时,
,则不等式
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69d88a41a8c39757a1bbcc8ae9052c67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66062dbd4978a7bb2fb9b9aabb898af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b03af66c2b6d916b41321d7bb292f1.png)
您最近一年使用:0次
2017-11-14更新
|
1569次组卷
|
2卷引用:湖北省襄阳市四校(襄州一中、枣阳一中、宜城一中、曾都一中)2017-2018学年高一上学期期中联考数学试题
2010·上海·二模
名校
10 . 已知二次函数
的图像为开口向下的抛物线,且对任意
都有
.若向量
,
,则满足不等式
的
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e04b4cd16224102ef696222caa56ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae81964a5d8df0502d6eaea575b11367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c461c17d03c12c75d64bcd7216e02c65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818155ef0386b3b18259bf458fd5a7bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次