名校
1 . 如图,在平面直角坐标系中,抛物线
与x轴交于点
,
与y轴交于点B,已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/3bef4347-1ebc-4993-87c2-71135bf5fecb.png?resizew=340)
(1)求抛物线的函数表达式;
(2)如图1,点P为抛物线上的点,且点P的横坐标为3,F是抛物线上异于点P的点,连接
,当
,求点F的横坐标;
(3)如图2,点Q为直线
上方抛物线上一点,
交
于点D,
交
于点E.记
,
,
的面积分别为
,
,
.求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2f117dc9adcb8fa7acf25bd2cbf283.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01831e1f8a6094abacfb2df3ceba7237.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/10/3bef4347-1ebc-4993-87c2-71135bf5fecb.png?resizew=340)
(1)求抛物线的函数表达式;
(2)如图1,点P为抛物线上的点,且点P的横坐标为3,F是抛物线上异于点P的点,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb630ea75318626934df0b44e40e7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05308b52fb64bb14d30105344aea32b9.png)
(3)如图2,点Q为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d57c5366753582457cc87de6e90b302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14d538e2d315324cd69bedc4b362485c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0aa4a44d13177b082ae3874dfdc6316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61561dcdd722c6fbe4447e6cec05c118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6398f2557943357934d2858366fdbb09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b2a89833c363fe06a5ae1524fa65144.png)
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2023-03-08更新
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380次组卷
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3卷引用:2023年福建省龙岩市长汀县中考一模数学试卷
名校
2 . 如图1,在矩形ABCD中,
,
,点E从点B出发,沿BC边运动到点C,连结DE,过点E作DE的垂线交AB于点F.
求证:
;
求BF的最大值;
如图2,在点E的运动过程中,以EF为边,在EF上方作等边
,求边EG的中点H所经过的路径长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf0a82ce7d7c3a93ce191d95ea23411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1745e89e942a6b9fde356ea7202a50e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f441e34a2e5788ef6e7bfd8eb058a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104e1834e64c70f2b2a6d48452f71b24.png)
![](https://img.xkw.com/dksih/QBM/2018/6/5/1960554969743360/1961704607350784/STEM/3740c5ac83454f0db139269f966942ec.png?resizew=320)
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2018-06-07更新
|
682次组卷
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2卷引用:【全国市级联考】福建省泉州市2018届九年级中考数学二模试题
真题
3 . 已知抛物线
与x轴只有一个公共点.
(1)若抛物线过点
,求
的最小值;
(2)已知点
中恰有两点在抛物线上.
①求抛物线的解析式;
②设直线l:
与抛物线交于M,N两点,点A在直线
上,且
,过点A且与x轴垂直的直线分别交抛物线和直线l于点B,C.求证:
与
的面积相等.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
(1)若抛物线过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee5813f73a29e35d3f8073811a8fa7fd.png)
①求抛物线的解析式;
②设直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cb59543ccf42b37ebce3f67416e561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad3e2b2689dfe97ec82d473ab6cf469.png)
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2021-06-28更新
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3828次组卷
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10卷引用:福建省2021年中考数学试卷
福建省2021年中考数学试卷(已下线)福建省2021年中考数学真题变式汇编5(已下线)押福建卷25题(二次函数综合)-备战2022年中考数学临考题号押题(福建卷)(已下线)专题05 二次函数(压轴题)-学易金卷:5年(2019-2023)中考1年模拟数学真题分项汇编(福建专用)(已下线)专题18 函数与线段、面积等最值问题【考点精讲】-【中考高分导航】备战2022年中考数学考点总复习(全国通用)江西省赣州市寻乌县2021-2022学年九年级上学期期末数学试题2022年安徽省初中学业水平考试第一模拟数学试题湖北省荆州市楚都中学2021-2022学年九年级下学期3月月考数学试题江西省赣州市寻乌县2022--2023学年九年级上学期期末检测数学试卷2022年河北省承德市承德县中考二模数学试题
4 . 结论:基本不等式
,当且仅当a=b时等号成立,它是解决最值问题的有力工具.
(1)我们可以利用所学的几何知识证明这个结论:
已知:在
中,
,点
为
的中点,
,垂足为
,设
,
,
求证:
;
![](https://img.xkw.com/dksih/QBM/2020/11/21/2597777184972800/2599728398843904/STEM/d6827ba5baa0430c969d8fc0b83d1d4c.png?resizew=192)
(2)可以直接利用(1)的结论,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72dc44cb9d5684d5377141fcd393c415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb51da4f2ef94f77f0b91872e1ebe73c.png)
(1)我们可以利用所学的几何知识证明这个结论:
已知:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e3f5dc11efe60b4fd9a13b1d6b83842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b9fb616a125f49b4b68057c62aa80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d96a29b9d2bbd5f043f4bcd8544010.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689f982af451283289255c87593ec338.png)
![](https://img.xkw.com/dksih/QBM/2020/11/21/2597777184972800/2599728398843904/STEM/d6827ba5baa0430c969d8fc0b83d1d4c.png?resizew=192)
(2)可以直接利用(1)的结论,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8488fbb958e42ec8e14b958a06b3adff.png)
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