“诗圣”杜甫出生在郑州巩义市笔架山下的窑洞里,窑洞是黄土高原、黄河中游特有的民居形式.如图,某窑洞口的底部为矩形,上部为抛物线.已知底部矩形的长为4米,宽为2米,窑洞口的最高点P离地面的距离为4米.
(1)请在图中建立适当的平面直角坐标系,并写出P点的坐标 .
(2)求(1)中所建坐标系中抛物线的表达式.
(3)若在窑洞口的上部安装一个矩形窗户
(窗户的边框忽略不计),使得点A,B在底部矩形的边上,点C,D在抛物线上,且
,那么这个窗户的宽
为多少米?
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/29/34c245ed-2920-430b-9435-719ef8cb90d6.png?resizew=141)
(1)请在图中建立适当的平面直角坐标系,并写出P点的坐标 .
(2)求(1)中所建坐标系中抛物线的表达式.
(3)若在窑洞口的上部安装一个矩形窗户
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5181b97a7e43959b8455680157c3b644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
更新时间:2024-03-29 11:54:31
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【推荐1】用长为78米的竹篱笆围一个面积为750平方米的长方形鸡场,鸡场的一边靠墙(墙长45米),另三边用竹篱笆围成.
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【推荐2】在矩形ABCD中,AD=6,AB=2
,点E是边AD上的一个动点,连接BE,以BE为一边在其左上方作矩形BEFG,过点F作直线AD的垂线,垂足为点H,连接DF.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/3/52d15cf8-eac4-41b6-87e9-272f6ad61849.png?resizew=398)
(1)当BE=EF时.
①求证:FH=AE;
②当
DEF的面积是
时,求线段DE的长;
(2)如图2,当BE=
EF,且射线FE经过CD的中点时,请直接写出线段FH长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/3/52d15cf8-eac4-41b6-87e9-272f6ad61849.png?resizew=398)
(1)当BE=EF时.
①求证:FH=AE;
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf6d7e0e75d0fb1aa7c89d7f1036fe46.png)
(2)如图2,当BE=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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【推荐1】已知:如图,抛物线
与
轴相交于两点
,
与
轴相交于点
,
![](https://img.xkw.com/dksih/QBM/2022/12/14/3130464889675776/3130684548767744/STEM/6f8ad2099fed4ca3afe4b5a3387f5af4.png?resizew=192)
(1)求抛物线的函数关系式;
(2)当
为何值时,
随
的增大而减小?
(3)若点
是抛物线
上一点,请求出
的值,并求出此时
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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![](https://img.xkw.com/dksih/QBM/2022/12/14/3130464889675776/3130684548767744/STEM/6f8ad2099fed4ca3afe4b5a3387f5af4.png?resizew=192)
(1)求抛物线的函数关系式;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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(3)若点
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【推荐2】如图,抛物线经过A(-3,0),B(-1,0),C(0,2)三点.
![](https://img.xkw.com/dksih/QBM/2021/10/14/2829173407457280/2829819310981120/STEM/8e66d982-4ca0-422c-9a25-8461281afae8.png)
(1)求抛物线的解析式;
(2)有一平行于x轴的直线MN交抛物线于MN两点,当线段MN=8时,求点M、N的坐标.
![](https://img.xkw.com/dksih/QBM/2021/10/14/2829173407457280/2829819310981120/STEM/8e66d982-4ca0-422c-9a25-8461281afae8.png)
(1)求抛物线的解析式;
(2)有一平行于x轴的直线MN交抛物线于MN两点,当线段MN=8时,求点M、N的坐标.
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【推荐1】某人定制了一批地砖,每块地砖(如图①所示)是边长为0.4米的正方形
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(2)
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(2)
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【推荐2】如图,一块矩形草地的长为
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【推荐3】某公司有一块如图所示的平行四边形ABCD的绿化地,中间四边形EFGH是正方形,种上甲类花;
AGD和
BEC是全等的等腰直角三角形,种上乙类花;
ABH和
CDF是全等的直角三角形,种上丙类花;三类花的价格如下表:
已知AH=3米,设BE的长为x米,绿化的总费用为y元.
(1)用含有x的代数式表示:EF= ,FD= ;
(2)求y关于x的函数解析式及x的取值范围;
(3)如果FD的长比CF至少多4米,求总费用y的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
花的种类 | 甲 | 乙 | 丙 |
价格(元/米2) | 200 | 100 | 150 |
(1)用含有x的代数式表示:EF= ,FD= ;
(2)求y关于x的函数解析式及x的取值范围;
(3)如果FD的长比CF至少多4米,求总费用y的最小值.
![](https://img.xkw.com/dksih/QBM/2020/12/28/2624003301359616/2624744873254912/STEM/fda040df-7ba9-4161-873a-a10da089fa14.png?resizew=469)
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