名校
1 . 在平面直角坐标系中,抛物线
(
)经过点
,
和
.
(1)求抛物线的表达式;
(2)若直线
与x轴交于点N,在第一象限内与抛物线交于点M,当
有最大值时,求出抛物线上点M的坐标;
(3)若点P为抛物线
(
))的对称轴上一动点,将抛物线向左平移1个单位长度后,Q为平移后抛物线上一动点,在(2)的条件下求得的点M,是否能与A,P,Q构成平行四边形?若能构成,求出Q点坐标;若不能构成,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623afc24f2227004b0e1b3922dfb954b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e705301752424a492f6277ed7774e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/17/c3757c69-7a2c-4abd-81e9-5adc7ef38cc5.png?resizew=149)
(1)求抛物线的表达式;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd9379845a75b3e4f6dd065ea360e1a.png)
(3)若点P为抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
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2 . 如图1,抛物线
交x轴于点
和点
,交y轴于点C.
(1)求抛物线的表达式;
(2)若点D是直线
上方拋物线上一动点,连接
,
和
,
交
于点M,设
的面积为
,
的面积为
,当
时,求点D的坐标;
(3)如图2,若点P是抛物线上一动点,过点P作
轴交直线
于Q点,请问在y轴上是否存在点E,使以P,Q,E,C为顶点的四边形是菱形,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/63d8de071a9c22c96a59b172d76c127e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f880f02c51a46e883522368a40ed66df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76da640bd19d2c87ad041fd44666de8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/16/638ff6e1-b039-49bc-a052-db1d5e40245e.png?resizew=355)
(1)求抛物线的表达式;
(2)若点D是直线
![](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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f9fba8a4098c1a0515286eb8d616dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f955e5cc9f108de6f3ca01e5eb84c52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779f538be94aff22b3eedabfc4c11be4.png)
(3)如图2,若点P是抛物线上一动点,过点P作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2784a52c4da98dc9df661fc152fc29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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3 . 如图,抛物线
经过
,
两点,与
轴交于另一点
.
![](https://img.xkw.com/dksih/QBM/2022/8/21/3049118349680640/3067740699205632/STEM/9933a4b1fc444fa38cb804bb9c7e7482.png?resizew=340)
(1)求此抛物线的解析式;
(2)若抛物线的顶点为
,点
为线段
上一动点
不与点
重合
,点
在线段
上移动,且
,设线段
,
,求
与
的函数关系式,并直接写出自变量
的取值范围;并直接写出
的值;
(3)在同一平面直角坐标系中,两条直线
,
分别与抛物线交于点
,
,与(2)中的函数图象交于点
,
问四边形
能否为平行四边形?若能,求
,
之间的数量关系;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833c997ef88d0b196eed775fbbf1c9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb06adb62c6ef820546d9cd71eb50516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2022/8/21/3049118349680640/3067740699205632/STEM/9933a4b1fc444fa38cb804bb9c7e7482.png?resizew=340)
(1)求此抛物线的解析式;
(2)若抛物线的顶点为
![](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/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ae75b8f7130997752d9ea34927d0d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf442f0f61ea476214bacfbb70ce379e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebefb66811e492c5067a7071410252f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e070f216d04e070e87d92b4f761cf66b.png)
(3)在同一平面直角坐标系中,两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1be7302f2e9ff02fee3fcf26e77b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa4ecbe57994125c6d4cf3b272c5e37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff2693fab4922833425c8daa73e1ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
4 . 已知抛物线
过点A(1,4)、B(
,0),过点A作直线AC∥x轴,交抛物线于另一点C,在x轴上有一点D(4,0),连接CD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/68f2b159-91c3-42f0-95ef-b82c44ab32da.png?resizew=388)
(1)求抛物线的表达式;
(2)若在抛物线上存在点Q,使得CD平分∠ACQ,请求出点Q的坐标;
(3)在直线CD的下方的抛物线上取一点N,过点N作NG∥y轴交CD于点G,以NG为直径画圆在直线CD上截得弦GH,问弦GH的最大值是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53be61cd85ec86aabd164cae0265246b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/68f2b159-91c3-42f0-95ef-b82c44ab32da.png?resizew=388)
(1)求抛物线的表达式;
(2)若在抛物线上存在点Q,使得CD平分∠ACQ,请求出点Q的坐标;
(3)在直线CD的下方的抛物线上取一点N,过点N作NG∥y轴交CD于点G,以NG为直径画圆在直线CD上截得弦GH,问弦GH的最大值是多少?
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名校
5 . 如图,抛物线
与x轴交于A(1,0),B(
,0)两点,C是抛物线与y轴的交点,P是该抛物线上一动点.
![](https://img.xkw.com/dksih/QBM/2022/7/9/3018948936974336/3040059723227136/STEM/311cb4249a8d4d11ad204a097cb97e72.png?resizew=170)
(1)求该抛物线的解析式;
(2)在(1)中抛物线的对称轴上求一点M,使得△MAC是以AM为底的等腰三角形,求出点M的坐标;
(3)设(1)中的抛物线顶点为D,对称轴与直线BC交于点E,过抛物线上的动点P作x轴的垂线交线段BC于点Q,使得D、E、P、Q四点组成的四边形是平行四边形?若存在,直接写出P点的坐标;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/81fb134b2b48acc99213fff6ccfee65f.png)
![](https://img.xkw.com/dksih/QBM/2022/7/9/3018948936974336/3040059723227136/STEM/311cb4249a8d4d11ad204a097cb97e72.png?resizew=170)
(1)求该抛物线的解析式;
(2)在(1)中抛物线的对称轴上求一点M,使得△MAC是以AM为底的等腰三角形,求出点M的坐标;
(3)设(1)中的抛物线顶点为D,对称轴与直线BC交于点E,过抛物线上的动点P作x轴的垂线交线段BC于点Q,使得D、E、P、Q四点组成的四边形是平行四边形?若存在,直接写出P点的坐标;若不存在,请说明理由.
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6 . 如图,平面直角坐标系中,O是坐标原点,抛物线
经过点
和点
与x轴另一个交点A.抛物线与y轴交于点C,作直线AD.
②并直接写出直线AD的函数表达式.
(2)点E是直线AD下方抛物线上一点,连接BE交AD于点F,连接BD,DE,
的面积记为
,
的面积记为
,当
时,求点E的坐标;
(3)点G为抛物线的顶点,将抛物线图象中x轴下方部分沿x轴向上翻折,与抛物线剩下部分组成新的曲线为
,点C的对应点
,点G的对应点
,将曲线
,沿y轴向下平移n个单位长度(
).曲线
与直线BC的公共点中,选两个公共点作点P和点Q,若四边形
是平行四边形,直接写出P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358e2987096a67189bcc2a642da39524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbdef5d0c05acbf63fa72fa85c5bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb4d0133c2f05b2d4e74cd6410869c1.png)
②并直接写出直线AD的函数表达式.
(2)点E是直线AD下方抛物线上一点,连接BE交AD于点F,连接BD,DE,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e64c953aaf341e772a5fe776fbc78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8060a00d925f27135a7baff2d0e9d598.png)
(3)点G为抛物线的顶点,将抛物线图象中x轴下方部分沿x轴向上翻折,与抛物线剩下部分组成新的曲线为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81722445de00f3cfcc3cb97e45b0d8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e9e7d734e2f0263b7586aa460983d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be1d24ecdf02d7c30eb7ff3f6933068.png)
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2022-06-28更新
|
1855次组卷
|
6卷引用:湖南省永州市宁远县禾亭中心校2021-2022学年八年级下期第三次月考 数学试卷
真题
名校
7 . 如图,在平面直角坐标系中,抛物线
与x轴交于A,B两点,与y轴交于点C,顶点为
,抛物线的对称轴交直线
于点E.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/d97ad912-938a-449c-9d5b-43fa8690f088.png?resizew=402)
(1)求抛物线
的表达式;
(2)把上述抛物线沿它的对称轴向下平移,平移的距离为
,在平移过程中,该抛物线与直线
始终有交点,求h的最大值;
(3)M是(1)中抛物线上一点,N是直线
上一点.是否存在以点D,E,M,N为顶点的四边形是平行四边形?若存在,求出点N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/71e2a819e635258ddb57edf5a3167306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/28/d97ad912-938a-449c-9d5b-43fa8690f088.png?resizew=402)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.png)
(2)把上述抛物线沿它的对称轴向下平移,平移的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93eaf59a9ff0f920616a94fcb163b19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)M是(1)中抛物线上一点,N是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2022-06-28更新
|
1348次组卷
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6卷引用:湖南省永州市宁远县至善学校2021-2022学年八年级下学期第三次月考数学试卷
湖南省永州市宁远县至善学校2021-2022学年八年级下学期第三次月考数学试卷2022年贵州省毕节市中考数学真题(已下线)22.1 二次函数的图象和性质-2022-2023学年九年级数学上册课后培优分级练(人教版)广东省汕尾市华大实验学校2022-2023学年九年级上学期第二次月考数学试题甘肃省张掖市甘州区第一中学2022-2023学年九年级下学期期中数学试题2023年贵州省遵义市九年级中考数学仿真模拟预测题
8 . 已知抛物线
的图象与x轴相交于点A和点
,与y轴交于点C,连接AC,有一动点D在线段AC上运动,过点D作x轴的垂线,交抛物线于点E,交x轴于点F,AB=4,设点D的横坐标为m.
(2)连接AE、CE,当
的面积最大时,点D的坐标是 ;
(3)当
时,在平面内是否存在点Q,使以B,C,E,Q为顶点的四边形为平行四边形?若存在,请求出点Q的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d8de071a9c22c96a59b172d76c127e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b47e7bf02b3ca16f7d96b9369e51a3.png)
(2)连接AE、CE,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0db2c49919467a2e14540f2aabd05cb.png)
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2022-05-21更新
|
288次组卷
|
4卷引用:湖南省长沙市中雅培粹学校2021-2022学年八年级下学期第三次月考数学试题
9 . 如图,在平面直角坐标系中,抛物线
交x轴于A、B两点(点A在点B左侧),交y轴于点C,一次函数y=kx+b(k≠0)与抛物线交于B、D两点,已知cos∠ABD=
.
![](https://img.xkw.com/dksih/QBM/2022/3/21/2940856386977792/2957285985837056/STEM/f3d68524-00e7-42b8-b464-351785679930.png?resizew=430)
(1)求点D的坐标;
(2)点F是抛物线的顶点,连接BF.P是抛物线上F、D两点之间的任意一点,过点P作PE∥BF交BD于点E,连接PF、PD、FE.求四边形PFED面积的最大值及相应的点P的坐标;
(3)连接AC,将抛物线沿射线AC方向平移
个单位长度得到新抛物线y',新抛物线与原抛物线交于点G.S是原抛物线对称轴上一点,T是平面内任意一点,G、S、A、T四点能否构成以AS为边的菱形?若能,请直接写出点T的坐标;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117c9e031f8bc140d18f27963595729e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://img.xkw.com/dksih/QBM/2022/3/21/2940856386977792/2957285985837056/STEM/f3d68524-00e7-42b8-b464-351785679930.png?resizew=430)
(1)求点D的坐标;
(2)点F是抛物线的顶点,连接BF.P是抛物线上F、D两点之间的任意一点,过点P作PE∥BF交BD于点E,连接PF、PD、FE.求四边形PFED面积的最大值及相应的点P的坐标;
(3)连接AC,将抛物线沿射线AC方向平移
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b947152b672cf56e5a8cde6800d71c0.png)
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2022-04-13更新
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4卷引用:湖南省永州市宁远县冷水镇云潭中学2021-2022学年八年级下学期第三次月考数学试卷
湖南省永州市宁远县冷水镇云潭中学2021-2022学年八年级下学期第三次月考数学试卷2022年重庆十八中两江实验中学九年级下学期第一次模拟数学试题2022年广东省珠海市第八中学中考第一次模拟考试数学试题(已下线)数学(广东省卷)-学易金卷:2023年中考考前押题密卷(含考试版、全解全析、参考答案、答题卡)
10 . 如图,抛物线
与x轴交于点A、B(点A在点B左侧),与y轴交于点C,连接BC.
![](https://img.xkw.com/dksih/QBM/2022/3/13/2935370954424320/2938843642183680/STEM/c32ebf00-0a69-4a78-8933-7a3db9f8ce23.png?resizew=225)
(1)求线段BC的长;
(2)过点A作AE//BC,与y轴交于点D,与抛物线第四象限的图象交于点E,P为抛物线上位于第一象限的点,连接PE交BC于点H,连接DH,求四边形PCDH面积的最大值及此时点P的坐标;
(3)将原抛物线沿射线BC方向平移
个单位长度得到抛物线y',y'与原抛物线交于点M,点N在直线BC上,且位于y轴右侧,在平面直角坐标系中是否存在点Q,使以点A、M、N、Q为顶点的四边形为菱形?若存在,请直接写出点Q的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3236d825b994ee9c28e5d5479a57b8ed.png)
![](https://img.xkw.com/dksih/QBM/2022/3/13/2935370954424320/2938843642183680/STEM/c32ebf00-0a69-4a78-8933-7a3db9f8ce23.png?resizew=225)
(1)求线段BC的长;
(2)过点A作AE//BC,与y轴交于点D,与抛物线第四象限的图象交于点E,P为抛物线上位于第一象限的点,连接PE交BC于点H,连接DH,求四边形PCDH面积的最大值及此时点P的坐标;
(3)将原抛物线沿射线BC方向平移
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
2022-03-18更新
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425次组卷
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2卷引用:湖南省永州市宁远县太平镇中心学校2021-2022学年八年级下学期第三次月考数学试卷