1 . 将一根长为
的铁丝首尾相接围成矩形,则该矩形面积的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 如图,某养殖户用
长的篱笆围成一个长方形养殖园,中间的两条篱笆隔离栏将这个长方形养殖园分割成三个较小的长方形,则围成养殖园的最大面积是______
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa95874b57afccaf193c257d437e5a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
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3 . 某小区计划建一个矩形花圃,花圃的一边利用长为
的墙,另三边及中间的隔断用总长为
的篱笆围成.围成的花圃是如图所示的矩形
,并在
边上留有两扇
宽的门.设
边的长为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
,矩形花圃的总面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
.
(1)求
与
之间的函数关系式;
(2)求自变量
的取值范围;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1611d15c7e1e4ab4a4a61537b3989d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d69b6eddd21064f4dcd7aee16edf6903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c901bcdfa58f0c68ad0161b0bab269.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/cc2a2cdc-e96e-4e14-876a-d64af43787da.png?resizew=202)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求自变量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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2023-11-24更新
|
99次组卷
|
2卷引用:江苏省连云港市灌云县2023-2024学年九年级上学期12月月考数学试题
4 . 用一条长
的绳子围成一个矩形,设矩形的一边长为
.
(1)若围成的矩形面积为
,求
的值;
(2)当
为何值时围成的矩形面积最大,最大面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57171806f407a98dd8a796d4d2d6bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
(1)若围成的矩形面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f44508a69ec50a20efabbe5ad12eaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2023-11-22更新
|
107次组卷
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5卷引用:清单12 二次函数与实际问题(10种题型解读+提升训练)-2023-2024学年九年级数学上学期期末考点大串讲(苏科版)
(已下线)清单12 二次函数与实际问题(10种题型解读+提升训练)-2023-2024学年九年级数学上学期期末考点大串讲(苏科版)广西壮族自治区玉林市容县2023-2024学年九年级上学期期中数学试题广西壮族自治区玉林市部分地区2023-2024学年九年级上学期期中阶段训练数学试题福建省漳州市芗城区厦门大学附属实验中学2023-2024学年九年级上学期月考数学试题广西壮族自治区玉林市2023-2024学年九年级上学期期中数学试题
5 . 如图,有长为24米的篱笆,一面利用墙(墙的最大可用长度为9米)围成中间隔有一道篱笆的长方形花圃.设花圃
边为x米,面积为y平方米.
(1)写出y与x的函数关系式______,并写出x的取值范围______;
(2)如果要围成面积为
的花圃,求
的长度;
(3)如果要使围成的花圃面积最大,求最大面积是多少
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/05eeef19-b5dd-405a-aa73-76b4fd6fb970.png?resizew=235)
(1)写出y与x的函数关系式______,并写出x的取值范围______;
(2)如果要围成面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbda3e2ba3d2e13f2a3e2e9af025aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)如果要使围成的花圃面积最大,求最大面积是多少
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba007666deb89951641bd1e24bc174a2.png)
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6 . 在2024年元旦即将到来之际,学校准备开展“冬日情暖,喜迎元旦”活动,小星同学对会场进行装饰.如图1所示,他在会场的两墙
、
之间悬挂一条近似抛物线
的彩带,如图2所示,已知墙
与
等高,且
、
之间的水平距离
为8米.
,
的高度是 米,抛物线的顶点坐标为 ;
(2)为了使彩带的造型美观,小星把彩带从点
处用一根细线吊在天花板上,如图3所示,使得点
到墙
距离为3米,使抛物线
的最低点距墙
的距离为2米,离地面2米,求点
到地面的距离;
(3)为了尽量避免人的头部接触到彩带,小星现将
到地面的距离提升为3米,通过适当调整
的位置,使抛物线
对应的二次函数的二次项系数始终为
,若设点
距墙
的距离为
米,抛物线
的最低点到地面的距离为
米,探究
与
的关系式,当
时,求
的取值范围.
![](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/372ad1814216fb7ebe39a0e067cf70be.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)为了使彩带的造型美观,小星把彩带从点
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)为了尽量避免人的头部接触到彩带,小星现将
![](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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ffd5c35bba71ea54c28622b6cf505d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef06a3c4befc30945469d55bea138bb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-11-18更新
|
435次组卷
|
6卷引用:数学(无锡卷)-学易金卷:2024年中考第一次模拟考试
7 . 用一段20米长的铁丝在平地上围成一个矩形,该矩形的一边长为x米,面积为y平方米,则y关于x的函数关系式为( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 如图,一面利用墙(墙的最大可用长度为
),用长为
的篱笆围成中间隔有一道篱笆的矩形花圃.设花圃的宽
的长为
,面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/14c43c22-3165-4771-8b18-d072a1ccdd4f.png?resizew=209)
(1)写出
与
之间的函数关系式及自变量x的取值范围.
(2)围成花圃的最大面积是多少?这时花圃的宽
等于多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b71bbf179a7e4f4a962e0e4b5b57b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0de66dee54a658c6bb7df2be47ecad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ffd001ed78d9a6617d6a17afb25c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4010da5b1fd07138d34cd7c2bd75bfd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/18/14c43c22-3165-4771-8b18-d072a1ccdd4f.png?resizew=209)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)围成花圃的最大面积是多少?这时花圃的宽
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2024-04-07更新
|
87次组卷
|
2卷引用:江苏省苏州市姑苏区南环实验中学校2022-2023学年九年级上学期12月考数学试题
9 . 如图,正方形
边长为10,
是直角三角形,
,点E是
边的动点,点F在
边上,当点E在线段
上移动时(点E不与A、D重合),设
,
的面积为y.
(1)当点E在线段
上移动时,
与
的关系会不会发生变化? 请简要说明理由;
(2)用含有x的代数式表示y;
(3)当点E运动到什么位置时,
的面积有最值?最值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff39c7aa648afd1080206c8080ff79e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33f381b03270154695d6b5421b1e739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c30f73c718bde8352055a14987fc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/c2dd8fb0-e96e-4892-a229-9c1ce6887a75.png?resizew=239)
(1)当点E在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66eae532e1a1551cfc7b5ff9cfc5aa9.png)
(2)用含有x的代数式表示y;
(3)当点E运动到什么位置时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
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名校
10 . 如图,一块空地(正方形
)的边长为
,按规划在空地中央准备建造一个宣传园(正方形
),留下四个全等的直角三角形做活动区(图中阴影部分),设
.
(1)当
取何值时,宣传园的面积是正方形
面积的58%;
(2)当
取何值时,宣传园的面积最小,最小面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c08094f72d5bd69246c453dd28e33d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94dca2c7f762a3eee32ff8874d8db11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/b6cc9b04-7285-4f79-aaf4-1cf2d1d908ee.png?resizew=127)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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