名校
1 . 如图1,直线
与x轴、y轴分别交于
、
两点,经过
、
两点的抛物线与x轴的另一交点坐标为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/20/04010a63-cc6b-47a8-aba3-11454f2bdfbd.png?resizew=312)
(1)求
、
两点的坐标及该抛物线所对应的函数关系式;
(2)P在线段
上的一个动点(与
、
不重合),过点P作直线
轴,交抛物线于点E,交x轴于点F,设点P的横坐标为m.
若点P的横坐标为m,请用m表示线段
的长度并写出m的取值范围;
②有人认为:当直线a与抛物线的对称轴重合时,线段
的值最大,你同意他的观点吗?请说明理由;
③过点P作直线
轴(图2),交
于点Q,那么在x轴上是否存在点R,使得
与
相似?若存在,请求出点R的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1882d2f789de61b5b7e3ec952e13b99e.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc4bcbc5fd831c4afadd53e3feddda1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/20/04010a63-cc6b-47a8-aba3-11454f2bdfbd.png?resizew=312)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)P在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/a6b2ed41dd71a90e1d68cfb84218263f.png)
![](https://img.xkw.com/dksih/QBM/2023/2/7/3169491648618496/3177968597467136/STEM/b8bb8644af954f839e721e34df68af50.png?resizew=11)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
②有人认为:当直线a与抛物线的对称轴重合时,线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
③过点P作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a0f6685d7c4b38f963c5549bb3cd6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7ffcd1925a2b1259221c6a476152f7.png)
您最近一年使用:0次
2023-02-19更新
|
333次组卷
|
3卷引用:山东省济宁市金乡县2022-2023学年下学期九年级第一次模拟学情检测数学试题
山东省济宁市金乡县2022-2023学年下学期九年级第一次模拟学情检测数学试题海南省海口市龙华区海南华侨中学2021-2022学年九年级上学期期末数学试题(已下线)专题17 代几综合压轴-学易金卷:2023年中考数学一模试题分项汇编(山东专用)
2 . 如图,已知抛物
与轴交于
,
两点,与y轴交于点C,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/f079e049-1f43-48bb-a2c5-d4cf2d39c4d1.png?resizew=206)
(1)求抛物线的解析式;
(2)若点P为线段
上的一动点(不与B、C重合),
轴,且交抛物线于点M,交x轴于点N,求
的面积的最大值;
(3)若点D为抛物线的顶点,在y轴上是否存在点E,使E到点B的距离与点E到点D的距离之差最大?若存在,请直接写出点E的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/f079e049-1f43-48bb-a2c5-d4cf2d39c4d1.png?resizew=206)
(1)求抛物线的解析式;
(2)若点P为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a9a8ae6c15072d8ae52b43c8edd9cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad3e2b2689dfe97ec82d473ab6cf469.png)
(3)若点D为抛物线的顶点,在y轴上是否存在点E,使E到点B的距离与点E到点D的距离之差最大?若存在,请直接写出点E的坐标;若不存在,请说明理由.
您最近一年使用:0次
3 . 如图,在平面直角坐标系中,
为等腰直角三角形,
,抛物线
经过A,B两点,其中点A,C的坐标分别为
,
,抛物线的顶点为点D.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/43c6fdb6-0eee-4acb-bf44-dc1044401afd.png?resizew=190)
(1)求抛物线的解析式;
(2)点E是直角
斜边
上的一个动点(不与A,B重合),过点E作x轴的垂线,交抛物线于点F,当线段
的长度最大时,求点E的坐标;
(3)在(2)的条件下,抛物线上是否存在一点P,使
是以
为直角边的直角三角形?若存在,直接写出所有点P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed10df4140819d5451773a45de66201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2f59980057f51e5cf3e86038cfaa16.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/43c6fdb6-0eee-4acb-bf44-dc1044401afd.png?resizew=190)
(1)求抛物线的解析式;
(2)点E是直角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c57b07f75e97d9f84718bd495ebcf4.png)
(3)在(2)的条件下,抛物线上是否存在一点P,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b51d3992644d37dc71c9b5a97d515c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
您最近一年使用:0次
4 . 如图,直线
分别交
轴、
轴于点
,过点
的抛物线
与
轴的另一交点为
,与
轴交于点
,抛物线的对称轴
交
于点
,连接
交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/4381ae2e-0126-4d80-80b5-57c5b2017e52.png?resizew=172)
(1)求抛物线的解析式;
(2)求证:
;
(3)
为抛物线上的一动点,直线
交
于点
,是否存在这样的点
,使以
为顶点的三角形与
相似?若存在,求点
的横坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aac6e5af2c04a7aa20466ab4dfab53e.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/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234618f50327655dac1e5c1de8e3e3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a299d2b999568e80be8005565ba209a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/4381ae2e-0126-4d80-80b5-57c5b2017e52.png?resizew=172)
(1)求抛物线的解析式;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/178e3fa2e4de57a4c067e79be7d798e7.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5e81031dc74ad0c3e22a18838967d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
5 . 如图,已知
,
,抛物线
经过
、
两点,交
轴于点
.点
是第一象限内抛物线上的一点,连接
,
.
为
上的动点,过点
作
轴,交抛物线于点
,交
于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/98cbc2df-a634-4b53-9938-f119509d3085.png?resizew=176)
(1)求抛物线的函数表达式;
(2)过点
作
,垂足为点
,设点
的坐标为
请用含
的代数式表示线段
的长,并求出当
为何值时
有最大值,最大值是多少?
(3)试探究
在运动过程中,是否存在这样的点
,使得以
,
,
为顶点的三角形与
相似.若存在,请求出此时点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ba5cbb31299d683ac6c7dd795db85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.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/1dc03fafb03395ed84030f03c5d93aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](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/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3a3db6d96518255f96ad7fc1ac98f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/98cbc2df-a634-4b53-9938-f119509d3085.png?resizew=176)
(1)求抛物线的函数表达式;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a6922808e9b59352c25c341cf23851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9c0002b13f6cae093cd9dc9f19941b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
(3)试探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bbf9680f74a9ac5d934304654ce2771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
名校
6 . 已知抛物线
与
轴交于
、
两点,与
轴交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/055faa8e-877e-4224-b9c0-1f5e2b30f2b1.png?resizew=213)
(1)求抛物线的表达式;
(2)点P在直线
下方的抛物线上,连接
交
于点
,过点
作
轴的垂线
,垂线
交
于点
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
垂线
,求证
;当
最大时,求点P的坐标及
的最大值;
(3)在(2)的条件下,在
上是否存在点
,使
是直角三角形,若存在,请直接写出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33355c289aba446bc7c892934b9c5a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323cf72ad438f1bcb37003ede7dd5237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21df2ff21377374dae306ce5895a46db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/055faa8e-877e-4224-b9c0-1f5e2b30f2b1.png?resizew=213)
(1)求抛物线的表达式;
(2)点P在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a9bfa68259d7a331be323b2038d628a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e719a13d708cba6a3298b08e8cb38ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a6ce188523ed6ab24fa2bfa6e17fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a6ce188523ed6ab24fa2bfa6e17fdb.png)
(3)在(2)的条件下,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b506b0941433a6a5d5387d0ec95596ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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2023-01-26更新
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212次组卷
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4卷引用:山东省济宁市曲阜市曲阜夫子学校2022-2023学年九年级上学期期末数学试题
山东省济宁市曲阜市曲阜夫子学校2022-2023学年九年级上学期期末数学试题2023年广东省江门市鹤山市沙坪中学中考二模数学试题(已下线)2023年佛山等市二模(二次函数综合)(已下线)湖北省襄阳五中华侨城实验学校2023-2024学年九年级8班上学期数学周测(13)
7 . 如图,抛物线
与 x 轴交于 A,B 两点,且
,与 y 轴交
于点 C,连接
,抛物线对称轴为直线
, D 为第一象限内抛物线上一动点,过点 D 作
于点 E,与
交于点 F,设点 D 的横坐标为 m.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/18320c24-2ca4-4086-8ee9-913e34713a7a.png?resizew=273)
(1)求抛物线的表达式;
(2)在抛物线的对称轴上是否存在点P,使得
的周长最小?若存在,求点P的坐标;
(3)在抛物线上是否存在点 D,使得
的面积最大,若存在,求出 m 的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0d44326c214c7a5ecc3068a29ec96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abef063e1692494fd4769d100f044b8.png)
![](https://img.xkw.com/dksih/QBM/2023/1/4/3145559524769792/3161266885246976/STEM/02e01ccbe5d5461f8c6eccaa50f4398e.png?resizew=7)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a179d6628345ad3442d2431d72f352a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504cf35247693ceb766c3b85a4ab2a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/18320c24-2ca4-4086-8ee9-913e34713a7a.png?resizew=273)
(1)求抛物线的表达式;
(2)在抛物线的对称轴上是否存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
(3)在抛物线上是否存在点 D,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
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名校
8 . 如图,在平面直角坐标系中,抛物线
经过点
,
,点P是直线
上的动点,过点P作x轴的垂线交抛物线于点M,设点P的横坐标为t.
![](https://img.xkw.com/dksih/QBM/2022/11/24/3116348575850496/3159024543522816/STEM/b0e08f62b87b46508e6964ccc6836a0f.png?resizew=248)
(1)求抛物线的解析式.
(2)若点P在第四象限,连接
,当线段
最长时,求
的面积.
(3)是否存在这样的点P,使得以点P、M、B、O为顶点的四边形为平行四边形?若存在,请直接求出点P的横坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5bd57912b194186fb5cbe63ed24861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d687d46701be07cae664d2f3112c561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ddd53df68c1ba8abbb3e37632d0b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://img.xkw.com/dksih/QBM/2022/11/24/3116348575850496/3159024543522816/STEM/b0e08f62b87b46508e6964ccc6836a0f.png?resizew=248)
(1)求抛物线的解析式.
(2)若点P在第四象限,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c013ea7e42e0e74601ac7bff6646ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
(3)是否存在这样的点P,使得以点P、M、B、O为顶点的四边形为平行四边形?若存在,请直接求出点P的横坐标;若不存在,请说明理由.
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2023-01-23更新
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3卷引用:山东省济宁学院附属中学2022-2023学年九年级下学期开学考试数学试题
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9 . 已知抛物线
的对称轴是直线
,与x轴相交于A,B两点(点B在点A右侧),与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/23/5d270e9f-5dfb-4af7-8ca3-42834faa104f.png?resizew=222)
(1)求抛物线的解析式和A,B两点的坐标;
(2)如图若点P是抛物线上B、C两点之间的一个动点(不与B、C重合),是否存在点P,使三角形
的面积最大?若存在,求点P的坐标及三角形
面积的最大值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f158fa81c5c6cece445ae2a24d08a34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/23/5d270e9f-5dfb-4af7-8ca3-42834faa104f.png?resizew=222)
(1)求抛物线的解析式和A,B两点的坐标;
(2)如图若点P是抛物线上B、C两点之间的一个动点(不与B、C重合),是否存在点P,使三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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10 . 如图,抛物线
与x轴交于点
,
,与y轴交于点A,点P是线段
上方抛物线上的一个动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/17/b970b52a-bdd3-4710-9687-3dfaf7e5c400.png?resizew=357)
(1)求抛物线的解析式;
(2)当点P运动到什么位置时,
的面积最大?
(3)过点P作x轴的垂线,交线段
于点D,再过点P作
轴交抛物线于点E,连接
.是否存在点P,使
为等腰直角三角形?若存在,求点P的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad97284da351a44c36c11d5cec429a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbdef5d0c05acbf63fa72fa85c5bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49dd31773f55719ebd91ed3389d0de68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/17/b970b52a-bdd3-4710-9687-3dfaf7e5c400.png?resizew=357)
(1)求抛物线的解析式;
(2)当点P运动到什么位置时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
(3)过点P作x轴的垂线,交线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf0215fcd72572bb524eca8a7fdc3f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
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2023-01-15更新
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159次组卷
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4卷引用:山东省济宁市金乡县2022-2023学年九年级上学期期末数学试题
山东省济宁市金乡县2022-2023学年九年级上学期期末数学试题江苏省盐城市东台市第四联盟2022-2023学年上学期九年级数学第二次阶段调查试题(已下线)江苏省盐城市东台市东台创新学校2022-2023学年九年级上学期第二次月考数学试题甘肃省酒泉市金塔县2022-2023学年九年级上学期期末考试数学试题