名校
1 . 如图1,在平面直角坐标系中,抛物线
与x轴交于
和
,与y轴交于点C,连接
.
(2)如图1,在x轴上有一动点D,平面内是否存在一点E,使以点A、D、C、E为顶点的四边形是菱形?若存在,请求出点E的坐标,若不存在,请说明理由.
(3)如图2,点M为抛物线上的一动点:
①若点M为直线
上方的抛物线上任意一点,过点M作y轴的平行线,交
于点N,过点M作x轴的平行线,交直线
于点Q,求
周长的最大值;
②若点M为抛物线上的任意一动点,且
,请直接写出满足条件的点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ffc79ad3c37fb879fb0b47f7a8da5f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f752d0257c9aae75e212755abc1b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc7d561b6e56aabf90e7c585c04f0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5345f892125374809bcaaab5da8d3f5f.png)
(2)如图1,在x轴上有一动点D,平面内是否存在一点E,使以点A、D、C、E为顶点的四边形是菱形?若存在,请求出点E的坐标,若不存在,请说明理由.
(3)如图2,点M为抛物线上的一动点:
①若点M为直线
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
②若点M为抛物线上的任意一动点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cf95a902ee77532760db3132a5877e.png)
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2 . 如图,抛物线
与x轴交于
,
两点,与
轴交于点
.
(1)求抛物线的解析式;
(2)若在线段
上存在一点
,使得
,过点
作
交
的延长线于点
,求点
的坐标;
(3)在(2)的条件下,点
是
轴正半轴上的一个动点,连接
,过
做
交
轴与
,
是
的中点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b50b33875af1433e9fa2de88530432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.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/2023/5/23/ad5e884c-3340-400a-9a09-e4ca4a4a758a.png?resizew=406)
(1)求抛物线的解析式;
(2)若在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8865cfc54688a0b6ef16241a7b97f2d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4372700e7f8e5c755c8ad71671224b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(3)在(2)的条件下,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0dd9872c8ff29ba1b2f889e224b3edf.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
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2023-05-11更新
|
337次组卷
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3卷引用:2023年山东省济南市天桥区中考二模数学试题
名校
3 . 如图1所示的矩形窗框
的周长及其两条隔断
、
的总长为
米,且隔断
、
分别与矩形的两条邻边平行,设
的长为
米,矩形
的面积为
平方米,
关于
的函数图像如图2,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/36be6e96-758e-425e-ad23-dd4b87fecb28.png?resizew=271)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/36be6e96-758e-425e-ad23-dd4b87fecb28.png?resizew=271)
A.矩形![]() | B.![]() ![]() ![]() |
C.当![]() ![]() | D.![]() |
您最近一年使用:0次
2023-05-09更新
|
372次组卷
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5卷引用:2023年陕西省宝鸡市陈仓区中考二模数学试卷
名校
4 . 要在某建筑物人字形屋顶上画一幅边框是矩形的画来美化,已知
,高线
,如图所示.
上,其余两个顶点分别在
上,求正方形的边长.
(2)若要使这幅画面积最大,且矩形的一边在
上,其余两个顶点分别在
上,
①设
,请用含
的代数式表示
的长;
②求此矩形的最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcca25052dcb5bb21dabf0a3bfafc123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72c70c8ea7bdc7a63fe262155e40526.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
(2)若要使这幅画面积最大,且矩形的一边在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d54431bbb28ebd98db5c1dc6083a75.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d54e3372c9910726f8bf06a966af997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
②求此矩形的最大面积.
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5 . 如图,用长为
的篱笆,一边利用墙(墙足够长)围成一个长方形花园,设花园的宽
为
,围成的花园面积为
,则y关于x的函数表达式为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d740004cfdade4c185f722dadc27e15.png)
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2023-07-14更新
|
193次组卷
|
5卷引用:广东省江门市开平市忠源纪念中学2022-2023学年九年级上学期11月期中数学试题
广东省江门市开平市忠源纪念中学2022-2023学年九年级上学期11月期中数学试题第26章 二次函数 26.3 实践与探索华东师大版(2012)九年级下册课前预习吉林省吉林市龙潭区亚桥第二九年制学校2022-2023学年九年级上学期期中数学试题吉林省长春市德惠市2023-2024学年九年级上学期期末数学试题(已下线)专题05用二次函数解决问题(3个知识点4种题型3个中考考点)-【帮课堂】2023-2024学年九年级数学下册同步学与练(苏科版)
6 . 如图,某农场要建一个矩形的菜园,菜园的一边
靠墙(墙长5m),另外三边
,
,
用木栏围成,木栏长8m.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/7d101fec-c6e0-443a-bbe1-0f0d6309fca6.png?resizew=113)
(1)求菜园的面积能达到
时的长和宽;
(2)菜园的最大面积是多少?
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/7d101fec-c6e0-443a-bbe1-0f0d6309fca6.png?resizew=113)
(1)求菜园的面积能达到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1cbadc94d4650c757e2db089879c9f1.png)
(2)菜园的最大面积是多少?
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名校
7 . 如图①,有一块三角形余料
,它的边
,高
.要把它加工成正方形零件,使正方形的一边在
上,其余两个顶点分别在
上,
交
于点E,则加工成的正方形零件的边长为多少?
![](https://img.xkw.com/dksih/QBM/2023/1/7/3147501178617856/3148394943676416/STEM/721a18cf22714d5bb3f370a7d2354654.png?resizew=441)
小颖解得此题的答案为
,小颖善于反思,她又提出了如下的问题:
(1)如果原题中所要加工的零件是一个矩形,且此矩形由两个并排放置的正方形组成.如图②,此时,这个矩形零件的相邻两边长又分别是多少?
(2)如果原题中所要加工的零件只是一个矩形,如图③,这样,此矩形零件的相邻两边长就不能确定,但这个矩形的面积有最大值,求这个矩形面积的最大值以及这个矩形面积达到最大值时矩形零件的相邻两边长又分别是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ebb33adb2310a6e03918761e68204a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267ace52b64e1e7dfc5211e033255b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://img.xkw.com/dksih/QBM/2023/1/7/3147501178617856/3148394943676416/STEM/721a18cf22714d5bb3f370a7d2354654.png?resizew=441)
小颖解得此题的答案为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad9de54606c4a72d0f8decb6b0e63b2.png)
(1)如果原题中所要加工的零件是一个矩形,且此矩形由两个并排放置的正方形组成.如图②,此时,这个矩形零件的相邻两边长又分别是多少?
(2)如果原题中所要加工的零件只是一个矩形,如图③,这样,此矩形零件的相邻两边长就不能确定,但这个矩形的面积有最大值,求这个矩形面积的最大值以及这个矩形面积达到最大值时矩形零件的相邻两边长又分别是多少?
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8 . 在周长为
的矩形铁片上剪去一个边长等于矩形宽
的等边三角形,设剩下的面积为
,求
与
的函数关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d51b21602ca6906279ecb645bfd12fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d740004cfdade4c185f722dadc27e15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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9 . 如图,在菱形
中,
,
,矩形
的四个顶点分别在菱形的四边上,则矩形
的最大面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/c1866af6-dfa5-4cae-861a-bf28daf20a7e.png?resizew=182)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32436704a722d5e568ff5c175bf3c662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17cb7a12bb8797615303fc20adb9f988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec780e86f57790cf88ec761e219bf5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/c1866af6-dfa5-4cae-861a-bf28daf20a7e.png?resizew=182)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-05-15更新
|
118次组卷
|
2卷引用:鲁教版(五四制)数学九年级上册第三章 二次函数单元检测
10 . 如图,在直角坐标系
中,抛物线
与
轴的正半轴相交于点
,与
轴的正半轴相交于点
,它的对称轴与
轴相交于点
,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/8a412032-e230-46de-96f6-9367b259f858.png?resizew=195)
(1)求此抛物线的表达式;
(2)如果点
在此抛物线上,
,垂足为
,
与线段
相交于点
,且
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cf77a054bc1e33f151cea26a7cceac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/17/8a412032-e230-46de-96f6-9367b259f858.png?resizew=195)
(1)求此抛物线的表达式;
(2)如果点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb73d10046e64d6f36e2dfdc9b9e6145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d02001b7a2644c91435dcda64b981d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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