1 . 如图,在平面直角坐标系中,点O为坐标原点,抛物线
与x轴交于点A,点B,与y轴交于点C,点A坐标为
.
(1)求抛物线的解析式;
(2)点P为第一象限抛物线上一点,连接PA交y轴交于D,设点P的横坐标为t,CD的长为d,求d关于t的函数解析式(不要求写出自变量t的取值范围);
(3)在(2)的条件下,将AP沿x轴翻折交抛物线于点Q,过点Q作y轴的平行线交PB的延长线于点E,过点E作
交y轴于点F,连接PF,若
,求直线PF的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc4f190441bb522737782e1912e9a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/18deea92-3848-472d-9592-769b3262b698.png?resizew=321)
(1)求抛物线的解析式;
(2)点P为第一象限抛物线上一点,连接PA交y轴交于D,设点P的横坐标为t,CD的长为d,求d关于t的函数解析式(不要求写出自变量t的取值范围);
(3)在(2)的条件下,将AP沿x轴翻折交抛物线于点Q,过点Q作y轴的平行线交PB的延长线于点E,过点E作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1330f18335dddd4ddc07961ec82a7f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68077800de4736172048c2d21bdbc6c3.png)
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2 . 如图所示,已知在平面直角坐标系
中,点
,点M是横轴正半轴上的一个动点,
经过原点O,且与
相切于点M.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/b5c63519-a636-4178-ae60-07f86c585475.png?resizew=148)
(1)当
轴时,点P的坐标为_____________ ;
(2)设点P的坐标为
,则y关于x的函数关系式为 _____________ (不用写出自变量x的取值范围);
(3)当射线
与直线
相交时,点M的横坐标t的取值范围是_____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc32b51af34f65636be5b0dc4810740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/b5c63519-a636-4178-ae60-07f86c585475.png?resizew=148)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd263fa65347735f95d3364e5b91a58.png)
(2)设点P的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
(3)当射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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真题
3 . 阅读下列材料:
在
中,
、
、
所对的边分别为
、
、
,求证:
.
证明:如图1,过点
作
于点
,则:
在
中, CD=asinB
在
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5409416f74ebf23e29be0d43e471629c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39a1ed1a08e09696c55fa0f69722570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcf9a85dda185f77d852e4b5444ac4e.png)
根据上面的材料解决下列问题:
中,
、
、
所对的边分别为
、
、
,求证:
;
(2)为了办好湖南省首届旅游发展大会,张家界市积极优化旅游环境.如图3,规划中的一片三角形区域需美化,已知
,
,
米,求这片区域的面积.(结果保留根号.参考数据:
,
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcf9a85dda185f77d852e4b5444ac4e.png)
证明:如图1,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3486ed44707198794c44eda7e9a591.png)
在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf8928aa8405e8c8a350f6f1285de3cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5409416f74ebf23e29be0d43e471629c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c39a1ed1a08e09696c55fa0f69722570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de0d10ef8b748d4531250c37c5d3f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcf9a85dda185f77d852e4b5444ac4e.png)
根据上面的材料解决下列问题:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3c65edad25ddd666cdce0d7e5afefc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/819ec21933abc80320ae0cb5d1a3592b.png)
(2)为了办好湖南省首届旅游发展大会,张家界市积极优化旅游环境.如图3,规划中的一片三角形区域需美化,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fed2f853e8635d113da0a8b30df61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb912c22248d8f21fc97f151e823091d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c5ff9c0671fb5f4afe00c5b7b1ed97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2082b0e4e457c2ea1e033d69d8b39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d90c44492f9dbc2a9b38aad7463825e2.png)
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2022-07-08更新
|
1315次组卷
|
10卷引用:专题14 解直角三角形-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)
(已下线)专题14 解直角三角形-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)2022年湖南省张家界市中考数学真题(已下线)专题14 解直角三角形-2022年中考数学真题分项汇编(全国通用)(第2期)(已下线)题型四 阅读理解题(已下线)第2讲 锐角三角函数与解直角三角形(已下线)第6讲 阅读题湖南省永州市宁远县2023-2024学年九年级下学期期中数学试题(已下线)查补重难点08 解直角三角形及其应用-【查漏补缺】2024年中考数学复习冲刺过关(江苏专用)山东省菏泽市成武县成武一中实验学校2022-2023学年九年级上学期12月月考数学试题山东省菏泽市成武一中实验学校2022-2023学年九年级上学期第一次学业评估测试数学试题
真题
4 . 阅读材料:十六世纪的法国数学家弗朗索瓦·韦达发现了一元二次方程的根与系数之间的关系,可表述为“当判别式
时,关于
的一元二次方程
的两个根
、
有如下关系:
,
”.此关系通常被称为“韦达定理”.已知二次函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/21/f6d9b482-6f00-402e-a407-991a5d49f51d.png?resizew=255)
(1)若
,
,且该二次函数的图象过点
,求
的值;
(2)如图所示,在平面直角坐标系
中,该二次函数的图象与
轴相交于不同的两点
、
,其中
、
,且该二次函数的图象的顶点在矩形
的边
上,其对称轴与
轴、
分别交于点
、
,
与
轴相交于点
,且满足
.
①求关于
的一元二次方程
的根的判别式的值;
②若
,令
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13abcbae584158e608b35cbf723d376.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/807d62d0b5623b3bd3cb285560bf8436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05dd02b6f561dcf94bab8a3160108d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897630dd340ec6c6b20cdd754d0a12c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd69aebdafb31468eb13ce3b28a36e47.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/21/f6d9b482-6f00-402e-a407-991a5d49f51d.png?resizew=255)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdb7a488910743dc5c63afb394b87e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)如图所示,在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a9e1eb4c3226489d1344321b10b7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec3d75e53b990bc8f9a4622928dd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b583230a32b774445332490c511989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7b0c34c4a6e7be6f08ef7b7829c4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ed1f2d0ca0876b96e1098192a33101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58876ba91cc1876127fde8467f2a7ebc.png)
①求关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fa32c1e926f40a0722d106563777ef.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a29217faf8dfc7b3dd0b7e1e89f4e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d68b9fa84e09146beee4c353ac0b76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
真题
5 . 如图,菱形ABCD的四个顶点均在坐标轴上,对角线AC、BD交于原点O,
于E点,交BD于M点,反比例函数
的图象经过线段DC的中点N,若
,则ME的长为( )
![](https://img.xkw.com/dksih/QBM/2021/6/22/2748338072797184/2748430049525760/STEM/eb8466b3-239c-42ed-84e4-453181c63f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f5dc11efe60b4fd9a13b1d6b83842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b66bfc4142107472444b28926b643e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eb3d1070981fed5ca65a34bb2282e6f.png)
![](https://img.xkw.com/dksih/QBM/2021/6/22/2748338072797184/2748430049525760/STEM/eb8466b3-239c-42ed-84e4-453181c63f18.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2021-06-22更新
|
1223次组卷
|
11卷引用:专题10 反比例函数-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)
(已下线)专题10 反比例函数-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)(已下线)专题12 函数综合-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)湖南省怀化市2021年中考真题数学试题(已下线)专题28.4+锐角三角函数(培优篇)(专项练习)-2021-2022学年九年级数学下册基础知识专项讲练(人教版)(已下线)(广东广州卷)2022年中考数学第一次模拟考试2022年四川省自贡市富顺县九年级下学期数学第二次练习题2022年贵州省玉屏侗族自治县九年级下学期第二次模拟考试数学试题2022年河南省南阳市镇平县九年级中招模拟训练数学试卷(二)2022年山东省聊城市东阿县中考三模数学试题(已下线)专题28.4 锐角三角函数(培优篇)(专项练习)-2022-2023学年九年级数学下册基础知识专项讲练(人教版)2023年广西壮族自治区玉林市玉州区中考一模数学试题
真题
解题方法
6 . 如图,抛物线
经过
,
两点,与
轴交于点
,连接
.
(2)如图2,直线
:
经过点A,点
为直线
上的一个动点,且位于
轴的上方,点
为抛物线上的一个动点,当
轴时,作
,交抛物线于点
(点
在点
的右侧),以
,
为邻边构造矩形
,求该矩形周长的最小值;
(3)如图3,设抛物线的顶点为
,在(2)的条件下,当矩形
的周长取最小值时,抛物线上是否存在点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cbd39cbef2bb66a619a90c772f0521.png)
?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0d44326c214c7a5ecc3068a29ec96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527adf33876b600568772d6ff0a91310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c044362183e52c9f684765b8a77fba0.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)如图2,直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023ab3a7eb0f59993c7608576e47c0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9c64cadaba1ccc1e06c62b4d68fc542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329c893cdaede883a62f613c46d86928.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
(3)如图3,设抛物线的顶点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43ac79e422ba4876949f0514c44539b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cbd39cbef2bb66a619a90c772f0521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1caeb4e336d644dfa93e5aff03dd903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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2021-06-21更新
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7卷引用:专题11 二次函数-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)
(已下线)专题11 二次函数-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)(已下线)专题12 函数综合-学易金卷:三年(2021-2023)中考数学真题分项汇编(湖南专用)湖南省岳阳市2021年中考数学真题(已下线)专题08 二次函数与矩形正方形存在性问题-挑战2022年中考数学压轴题之学霸秘笈大揭秘湖南省永州市宁远县2023-2024学年九年级下学期期中数学试题2022年山东省聊城市临清市九年级第二次模拟考试数学试题2022年天津市红桥区九年级三模数学试题
7 . 如图,直线l:y=﹣
x+2与x轴交于点A,与y轴交于点B,C为线段OA的一个动点,以A为圆心,AC长为半径作⊙A,⊙A交AB于点D,连接OD并延长交⊙A于点E,连接CD.
(1)当AC=2时,证明:△OBD是等边三角形;
(2)当△OCD∽△ODA时,求⊙A的半径r;
(3)当点C在线段OA上运动时,求OD•DE的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/df385fdf-028f-4116-addf-dfe04de3b53f.png?resizew=180)
(1)当AC=2时,证明:△OBD是等边三角形;
(2)当△OCD∽△ODA时,求⊙A的半径r;
(3)当点C在线段OA上运动时,求OD•DE的最大值.
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