1 . 如图(1)是一个高脚杯的截面图,杯体
呈抛物线形(杯体厚度不计),杯底
,点O是
的中点,
,杯子的高度(即
,
之间的距离)为
,
所在直线为x轴,
所在直线为y轴建立平面直角坐标系(1个单位长度表示
).
所在抛物线的解析式;
(2)将杯子向右平移
,并倒满饮料,杯体
与y轴交于点E(图2),过D点放一根吸管,吸管底部碰触到杯壁后不再移动,发现剩余饮料的液面低于点E,设吸管所在直线的解析式为
,求k的取值范围;
(3)将放在水平桌面/上的装有饮料的高脚杯绕点B顺时针旋转60°,液面恰好到达点D处(
),如图3.
①请你以
的中点O为原点,
所在直线为x轴,
所在直线为y轴建立平面直角坐标系;
②请直接写出此时杯子内液体的最大深度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c97bc6d754ac8cfbc7d5576edbb81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff65ab4ec507ada90acb8755fbd189c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca8f73cfdda94570923320def7885910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc31bf4b6ed8cf336432a5a2791e67e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048b61a5fb5f420c6d7de88db5bc3aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c97bc6d754ac8cfbc7d5576edbb81a.png)
(2)将杯子向右平移
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78d0ab561d0c9bb9099772c596af8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c97bc6d754ac8cfbc7d5576edbb81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
(3)将放在水平桌面/上的装有饮料的高脚杯绕点B顺时针旋转60°,液面恰好到达点D处(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20ea459c1598da5a060d240d72f6d88.png)
①请你以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
②请直接写出此时杯子内液体的最大深度.
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2 . 在锐角
中,
,矩形
的两个顶点
,
分别在
上,另两个顶点
均在
上,高
交
于点
,设
的长为
,矩形
的面积为
.
的长,并用含
的式子表示线段
的长;
(2)请求出
关于
的函数解析式;
(3)试求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c121954e50fc6f33829a52a782720e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1e5bbf051d2feb8f123c3ca05b5fa9.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/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1e5bbf051d2feb8f123c3ca05b5fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)请求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)试求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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3 . 如图所示,
为等腰直角三角形,
,正方形
边长也为2,且
与
在同一直线上,
从C点与D点重合开始,沿直线
向右平移,直到点A与点E重合为止,设
的长为
,
与正方形
重合部分(图中阴影部分)的面积为y,则y与x之间的函数关系的图象大致是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6baeb4763aeb5c65b9aeee8e5c49e1c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2257da1e2425f2ea9ac7440f52659ff.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
4 . 图1是某校园的紫藤花架,图2是其示意图,它是以直线
为对称轴的轴对称图形,其中曲线
,
,
,
均是抛物线的一部分.
,
到地面距离分别为5米和4米.曲线
的最低点到地面的距离是4米,与点
的水平距离是3米;曲线
的最低点到地面的距离是
米,与点
的水平距离是4米.
素材2:按图3的方式布置装饰灯带
,
,
,
,
,布置好后成轴对称分布,其中
,
,
,
垂直于地面,
与
之间的距离比
与
之间的距离多2米.
(1)任务一:(1)在图2中建立适当的平面直角坐标系,求曲线
的函数解析式;
(2)任务二:(2)若灯带
长度为
米,求
的长度.(用含
的代数式表示);
(3)任务三:(3)求灯带总长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2148ddb09d551d09a0d93decdf401bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
素材2:按图3的方式布置装饰灯带
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19247393d6b9122742a1a926ff495314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae57e49b519bb89ea02274318a34438d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14e444150bc60e96a5973b4209a4c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19247393d6b9122742a1a926ff495314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae57e49b519bb89ea02274318a34438d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14e444150bc60e96a5973b4209a4c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19247393d6b9122742a1a926ff495314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14e444150bc60e96a5973b4209a4c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae57e49b519bb89ea02274318a34438d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(1)任务一:(1)在图2中建立适当的平面直角坐标系,求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)任务二:(2)若灯带
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(3)任务三:(3)求灯带总长度的最小值.
您最近一年使用:0次
5 . 综合与实践
素材:一张边长为4的正方形纸片
步骤1:对折正方形纸片
,使
与
重合,得到折痕
,把纸片展平.
步骤2:再一次折叠纸片,点
落在点
处,并使折痕经过点
,得到折痕
,点
在边
上,过点
作
的垂线交射线
于点
.
落在边
上,直接写出
的度数;
(2)如题2图,设
,
,试求
关于
的函数表达式;
(3)如题3图,
为
的外接圆,若
与边
相切,求
的长.
素材:一张边长为4的正方形纸片
步骤1:对折正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
步骤2:再一次折叠纸片,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ffcf0b442d5ff2ce8efa1a778b4ecd6.png)
(2)如题2图,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8711eddf26d11fc974dfb6da4b640918.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9a1962f7c0143fef5d3e98075e852a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)如题3图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729684f958ad60b8e905fe1e1da53c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
您最近一年使用:0次
名校
6 . 问题情境:
“综合与实践”课上,老师让同学们以“矩形的翻折”为主题开展数学活动.
第1步:有一张矩形纸片
,在
边上取一点
沿
翻折,使点
落在矩形内部
处;
第2步:再次翻折矩形,使
与
所在直线重合,点
落在直线
上的点
处,折痕为
.
翻折后的纸片如图1所示
的度数为____________;
(2)若
,求
的最大值;
拓展应用:
(3)一张矩形纸片通过问题情境中的翻折方式得到如图2所示的四边形纸片
,其中
的一边与矩形纸片的一边重合,
,
,求该矩形纸片的面积.
“综合与实践”课上,老师让同学们以“矩形的翻折”为主题开展数学活动.
第1步:有一张矩形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
第2步:再次翻折矩形,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3f7368811340328acf5be13f499d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3f7368811340328acf5be13f499d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
翻折后的纸片如图1所示
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ffab06abe01c9b48aa4692c73d8b7c6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7288ae412a2147cbc2cef4294538476d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
拓展应用:
(3)一张矩形纸片通过问题情境中的翻折方式得到如图2所示的四边形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13120e2133d0ba64f06aa6e82a560fbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6992b3bcc99e2ed0fe91ddb21b63c561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2961788d557835a374fd2a496271834e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f464d174064bab081d6d1b9240d887db.png)
您最近一年使用:0次
2024-04-22更新
|
346次组卷
|
3卷引用:2024年江苏省南通市海安市九年级中考一模数学试题
7 . 如图,在平面直角坐标系
中,已知点
、点
,抛物线
经过点
,且顶点
在线段
上(与点
、
不重合).
、
的值;
(2)将抛物线向右平移
(
)个单位,顶点落在点
处,新抛物线与原抛物线的对称轴交于点
,连接
,交
轴于点
.
①如果
,求
的面积;
②如果
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d1e4a02f6a99a4b838dcaf9541d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6938eeb65411eeac15e140cf1db99773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(2)将抛物线向右平移
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
①如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b996e05aecd15a1416b8475c73c02c3c.png)
②如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04a4fd8819efcaf01ef8cf6f485e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-04-22更新
|
275次组卷
|
3卷引用:2024年上海市松江区中考二模数学试题
2024年上海市松江区中考二模数学试题数学(长春卷)-【试题猜想】2024年中考考前最后一卷(已下线)专题13 压轴24题二次函数综合60题专练(含上海24年最新模拟题)-2024年中考数学毕业班二轮热点题型归纳与变式演练(上海专用)
8 . 如图,某劳动小组借助一个直角墙角围成一个矩形劳动基地
,墙角两边
和
足够长,用总长
的篱笆围成另外两边
和
.有下列结论:
的长是
时,劳动基地
的面积是
;
②
的长有两个不同的值满足劳动基地
的面积为
;
③点
处有一棵树(树的粗细忽略不计),它到墙
的距离是
,到墙
的距离是
,如果这棵树需在劳动基地内部(包括边界),那么劳动基地面积的最大值是
,最小值是
.
其中,正确结论的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2fc57da7f8399eae9ad9ad22ca836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e6e41ac221847824a72e964f340f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6307c0249ba768c1c0c9a253c31720d2.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb92c9032804326713c7b4feea53f40.png)
③点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e978c77cb0d7eff794447241e9829867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea92883fe24b097c9a881ef8c92eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a796b826cc01a89d10f83be5e29d7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fb5474bdc74da700b463eabd05bd8e.png)
其中,正确结论的个数是( )
A.0 | B.1 | C.2 | D.3 |
您最近一年使用:0次
9 . 已知抛物线
(
)与
轴交于
,
两点(点
在点
左边),与
轴交于点
.
(1)若点
在抛物线上.
①求抛物线的解析式及点
的坐标;
②连接
,若点
是直线
上方的抛物线上一点,连接
,
,当
面积最大时,求点
的坐标及
面积的最大值;
(2)已知点
的坐标为
,连接
,将线段
绕点
顺时针旋转
,点
的对应点
恰好落在抛物线上,求抛物线的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/387cf772ee84a0756a97b403a5cfcf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac9eb4f13a6ec140f7050e8d7dde52c.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27814a264126a21491c1963346b176a.png)
①求抛物线的解析式及点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a33cd211f77152e153f404e58a04d77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350e954f629c1901a5cec03558319e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
10 . 综合运用
如图,在
中,
,过点
作
的垂线段
,垂足为
,连接
,且
.
的长.
(2)以点
为中心,按逆时针方向旋转
一周,使旋转后得到的
的边
恰好经过点
(点
不与点
重合),求此时旋转角的度数.
(3)在(2)的条件下,将
沿
向右平移
个单位长度,设平移后的图形与
重叠部分的面积为
,当
时,求
与
的函数关系式.
如图,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f1a7fd813b91c129c8542aa9cb9262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d030bc03d5e8e2bbd79de338a7c375ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7bf58e5fea1189b33cf55d86335452f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d554c15e8b2a3c9ecbe49710fb9bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b3e7b410f13b37f3e70e45f5e91fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3bb972d11120544991d4b4e9c197c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9164f4960138235f404ee565bf9f7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
(3)在(2)的条件下,将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3bb972d11120544991d4b4e9c197c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41663d9e5e18891475aeaa98794f33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0dc09e17531cf57e0f8756aa146057b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次