名校
1 . 如图,五边形ABCDE为一块土地的示意图.四边形AFDE为矩形,
米,
米,BC截
交AF、FD分别于点B、C,且
米.
(1)现要在此土地上划出一块矩形土地
作为安置区,若设
的长为x米,矩形
的面积为y平方米,求y与x的函数关系式,并求当x为何值时,安置区的面积y最大,最大面积为多少?
(2)因三峡库区移民的需要,现要在此最大面积的安置区内安置30户移民农户,每户建房占地100平方米,政府给予每户4万元补助,安置区内除建房外的其余部分每平方米政府投入100元作为基础建设费,在五边形
这块土地上,除安置区外的部分每平方米政府投入200元作为设施施工费.为减轻政府的财政压力,决定鼓励一批非安置户到此安置区内建房,每户建房占地120平方米,但每户非安置户应向政府交纳土地使用费3万元.为保护环境,建房总面积不得超过安置区面积的
.若除非安置户交纳的土地使用费外,政府另外投入资金150万元,请问能否将这30户移民农户全部安置?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3989d22a6df91172aacf8d56c53c658a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ad017fe24983d4b6e0b26929fd2e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e8c257f5615d30660cef4157c6b273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b761620d4118d328135400b9f66540e2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/26/cc1ad4ca-66df-4842-a1c0-febf460c4422.png?resizew=184)
(1)现要在此土地上划出一块矩形土地
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61df5649512eb5736d398c45a3dc4b07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61df5649512eb5736d398c45a3dc4b07.png)
(2)因三峡库区移民的需要,现要在此最大面积的安置区内安置30户移民农户,每户建房占地100平方米,政府给予每户4万元补助,安置区内除建房外的其余部分每平方米政府投入100元作为基础建设费,在五边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1065ae0947705c7d16a5a86c78f07e.png)
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2 . 如图1,在平面直角坐标系中,抛物线
交x轴于
、
两点,交y轴于点C,连接
,直线
解析式为
.
(1)a= ;b= ;k= ;m= .
(2)如图2.点P为线段
上方的抛物线上一动点,点F为x轴上一个动点,连接
、
,当
面积最大时,求
的最小值,并求出此时P点的坐标.
(3)在(2)的条件下,将抛物线向右移两个单位,再向上移两个单位,得到新抛物线,点E是新抛物线对称轴上一点,点N是新抛物线上一点,直接写出所有使得以点B、P、N、E为顶点的四边形是平行四边形的点N的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ceba6b11658f2cc227b1f550ba25c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a525534689bd2701205d4ab17574c39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/8/694af18b-ae87-44f8-86cf-fe3182e69eee.png?resizew=347)
(1)a= ;b= ;k= ;m= .
(2)如图2.点P为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e55d3700177e4eae9215e2c2d4a8b6.png)
(3)在(2)的条件下,将抛物线向右移两个单位,再向上移两个单位,得到新抛物线,点E是新抛物线对称轴上一点,点N是新抛物线上一点,直接写出所有使得以点B、P、N、E为顶点的四边形是平行四边形的点N的坐标.
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3 . 直线l:
与x轴、y轴分别交于点A、B,拋物线
的顶点为P,且与x轴交点为O、C.
(1)如图,若
.
① 当点P在直线
上时,求m的值;
② 若抛物线在
的范围内,至少存在一个x的值,使
,求m的取值范围.
(2)过P作
于H,令
.
①求出S与m的函数关系式,并写出自变量m的取值范围;
②分别求出当
与
时m的值(直接写出结果).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95c6373184f483f4c9422a9a6883bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfed4a7eca53bbc25c1f75e671b80f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/632a51d1-ec7f-4c26-b44e-6d28a4dc6f7d.png?resizew=332)
(1)如图,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0296b1ec0cee710e8e505aa8a5b07e15.png)
① 当点P在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08400f8bd1f5b4c044fe6b911f31ee3d.png)
② 若抛物线在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ead95cd3abf3da4beef4acc9fc345b5.png)
(2)过P作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b82ad29eced82f21e42ac9e795a892c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2abd3a9827db2689e74fdfc9b147b6.png)
①求出S与m的函数关系式,并写出自变量m的取值范围;
②分别求出当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86c12d115738a72e82820469318ec62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f91525de979d58b1580892b431faf3a.png)
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4 . 在平面直角坐标系中,抛物线
与
轴交于
、
两点(点
在点
的左侧),与
轴交于点
.
![](https://img.xkw.com/dksih/QBM/2023/5/13/3236682362486784/3239801309954048/STEM/cd37e81e6487431e9b05d1ce0d043c00.png?resizew=255)
(1)若点
在抛物线上,求抛物线的解析式及
点的坐标;
(2)在(1)的条件下,点
是直线
上方抛物线上一点,
于
,直线
交
轴于点
,求线段
的最大值及此时点
的坐标;
(3)令抛物线的顶点为
,若
是锐角三角形,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d039de5bf810e3ff6b0b6096fa48d462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.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)
![](https://img.xkw.com/dksih/QBM/2023/5/13/3236682362486784/3239801309954048/STEM/cd37e81e6487431e9b05d1ce0d043c00.png?resizew=255)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7009abd510b8ce6fd7cb3a7b342ca1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6b93dbe5272a5167ff4e2918bec864.png)
(2)在(1)的条件下,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829fc6685b59fdc609f32f30ebd9e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)令抛物线的顶点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92905d020164683947943040ec19c530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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5 . 在平面直角坐标系中,直线
与
轴,
轴分别交于
,
两点,顶点为
的抛物线
与
轴交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/28a90388-8a4e-4b76-8a92-f5708cc97e88.png?resizew=267)
(1)如图,当
时,点
是抛物线
段上的一个动点.
①求
,
,
,
四点的坐标;
②当
面积最大时,求点
的坐标;
(2)在
轴上有一点
,当点
在线段
上时,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54467455f7d47b6eec081e57623fbf34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d9bad316c46abca19dc97bea825df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/16/28a90388-8a4e-4b76-8a92-f5708cc97e88.png?resizew=267)
(1)如图,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
①求
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85f5b4b7bc0462b570a9f8a84f08fff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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6 . 如图,正方形
的边长为5,E为
上一动点,连接
,
,以
为边向右侧作正方形
.
①若
,则正方形
的面积为_________ .
②连接
,
,则
面积的最小值为_________ .
![](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/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1f13007c6d134c50004c62dc240707.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f95e892ce723ab9959afb995ea3773e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1f13007c6d134c50004c62dc240707.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029ad83f1a3262048cba0e650b63e929.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/17/2617bfa8-bcab-4513-8d0c-98851235b781.png?resizew=148)
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2023-10-02更新
|
100次组卷
|
3卷引用:湖北省随州市曾都区2021-2022学年九年级上学期期末数学试题
湖北省随州市曾都区2021-2022学年九年级上学期期末数学试题河北省邯郸市凌云中学2022--2023学年九年级上学期期中数学试题(已下线)专题10 二次函数(十二大题型)-【好题汇编】备战2023-2024学年九年级数学上学期期末真题分类汇编(山东专用)
7 . 如图,抛物线
与x轴交于
两点,与y轴交于点C,连接
.点P是第四象限内抛物线上的一个动点,点P的横坐标为m,过点P作
轴,垂足为点M,
交
于点Q,过点P作
交x轴于点E,交
于点F.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/7/a26094f2-8170-4bf5-ab9c-9cc8100231f3.png?resizew=212)
(1)求抛物线的解析式:
(2)试探究在点P运动的过程中,是否存在这样的点Q,使得以A,C,Q为顶点的三角形是等腰三角形.若存在,请直接写出 此时点Q的坐标;若不存在,请说明理由;
(3)请用含m的代数式表示线段
的长,并求出m为何值时
有最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b286a72a818ccc52e63581841da08dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7ab346653b62d2bc08438da5e9a82e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5345f892125374809bcaaab5da8d3f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d60f55c585f1b455027202684b13e7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/7/a26094f2-8170-4bf5-ab9c-9cc8100231f3.png?resizew=212)
(1)求抛物线的解析式:
(2)试探究在点P运动的过程中,是否存在这样的点Q,使得以A,C,Q为顶点的三角形是等腰三角形.若存在,请
(3)请用含m的代数式表示线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
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名校
8 . 如图,利用一面墙
墙的长度为
,用
长的篱笆围成两个鸡场,中间用一道篱笆隔开,每个鸡场均留一道
宽的门,设
的长为
米.
(1)若两个鸡场的面积和为S,求S关于
的关系式;
(2)两个鸡场面积和S有最大值吗?若有,最大值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab144fd3ef902f337b2a81dac990a062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31962c08f3858c22a4937ef2d955dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f328ba89c0a92a4447788b65571f7aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/16/ff92e3a6-ae70-41b5-9fb1-3c619b902b92.png?resizew=211)
(1)若两个鸡场的面积和为S,求S关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)两个鸡场面积和S有最大值吗?若有,最大值是多少?
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2023-09-15更新
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4卷引用:2022年湖北省武汉市新洲区阳逻街一中中考模拟数学试题
2022年湖北省武汉市新洲区阳逻街一中中考模拟数学试题湖北省咸宁市2023-2024学年九年级上学期月考数学试题湖北省孝感市三校联考2023-2024学年九年级上学期月考数学试题(已下线)22.2+二次函数与实际问题(题型精讲精练)1(原卷版)
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9 . 春回大地,万物复苏,又是一年花季到.某花圃基地计划将如图所示的一块长40 m,宽20 m的矩形空地划分成五块小矩形区域.其中一块正方形空地为育苗区,另一块空地为活动区,其余空地为种植区,分别种植A,B,C三种花卉.活动区一边与育苗区等宽,另一边长是10 m.A,B,C三种花卉每平方米的产值分别是2百元、3百元、4百元.
,花卉B的种植面积是______
,花卉C的种植面积是_______
.
(2)育苗区的边长为多少时,A,B两种花卉的总产值相等?
(3)若花卉A与B的种植面积之和不超过
,求A,B,C三种花卉的总产值之和的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dddf656285f15a7ec64b2e9dae3619f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dddf656285f15a7ec64b2e9dae3619f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dddf656285f15a7ec64b2e9dae3619f.png)
(2)育苗区的边长为多少时,A,B两种花卉的总产值相等?
(3)若花卉A与B的种植面积之和不超过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/593e8f9ec13a4d1a42d894bf1b65c36d.png)
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11卷引用:湖北省武汉市部分学校2022~2023学年九年级下学期四月调考数学试卷
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10 . 如图,等腰直角三角形
的直角边与正方形
的边长都为
,且在同一直线上,开始时A点与M点重合,让
向右平移,直到点C与点N重合.设阴影部分面积为
,
的长为
,则y与x之间的函数关系的图象大致是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/7/079d0526-c6d8-41da-9319-fa6ab18e2898.png?resizew=134)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eacd892f03da01942140679667792250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da6a52e3eb6cef810c7770b8e53fdcf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/7/079d0526-c6d8-41da-9319-fa6ab18e2898.png?resizew=134)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-06更新
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4卷引用:2023年湖北省黄冈市浠水县兰溪镇河口初级中学中考一模数学试题