如图,抛物线
与x轴交于A,B两点,点A在点B的左侧,抛物线与y轴交于C,抛物线的顶点为D,直线
过点C交x轴于
.
(1)写出顶点D的坐标和直线
的解析式.
(2)点Q在x轴的正半轴上运动,过Q作y轴的平行线,交直线
于M,交抛物线于N,连接
,将
沿
翻转,M的对应点为
.探究:是否存在点Q,使得
恰好落在y轴上?若存在,请求出Q的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f43c0a8b8e17b8f7923f1baa4dce03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbc36c30fe8687f968ae81b7abee92c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/8/d8919c68-fd03-42cc-ab4c-69b91b239510.png?resizew=306)
(1)写出顶点D的坐标和直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)点Q在x轴的正半轴上运动,过Q作y轴的平行线,交直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12225a1a1eda07908309f8100cc34726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
更新时间:2023-05-22 18:21:34
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解答题-证明题
|
较难
(0.4)
【推荐1】如图,已知点
和点
都在一次函数
上,
是
的平分线,过点
作
,垂足为点
,过点
作
轴的垂线,垂足为
.
(1)求这条直线的解析式;
(2)求证:
为
的中点;
(3)若一次函数图像上有点
,和点
,
,
构成梯形,试求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7dc24c48d8b988443cc189488e8185d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bda45b7f565147f18a5c83bb8a23142.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a457b899731577bfe61dda594ae4eec4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09785a454d62cbbd2e16ed61ed172a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/8/a90f2f3b-0a76-4f6e-ad4b-6369fe8d7589.png?resizew=240)
(1)求这条直线的解析式;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
(3)若一次函数图像上有点
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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解答题-问答题
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【推荐2】在平面直角坐标系中,已知点
,
,
,直线
经过点
,抛物线
恰好经过
,
,
三点中的两点.
(1)判断点
是否在直线
上,并说明理由;
(2)求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/466e8c438084aef563c6aaeff3bca583.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75929925842ca723b34647ccaa596cdf.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/c5db41a1f31d6baee7c69990811edb9f.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54479885d4ab2f717d2e97718da04b43.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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真题
【推荐1】如图,在边长为2的正方形ABCD中,G是AD延长线上的一点,且DG=AD,动点M从A出发,以每秒1个单位的速度沿着A→C→G的路线向G点匀速运动(M不与A、G重合),设运动时间为t秒.连接BM并延长交AG于N.
![](https://img.xkw.com/dksih/QBM/2015/7/9/1573868115787776/1573868122120192/STEM/54dbc9c564dd48c4a78fc2b44aaa2b27.png)
(1)是否存在点M,使△ABM为等腰三角形?若存在,分析点M的位置;若不存在,请说明理由;
(2)当点N在AD边上时,若BN⊥HN,NH交∠CDG的平分线于H,求证:BN=NH;
(3)过点M分别用AB、AD的垂线,垂足分别为E、F,矩形AEMF与△ACG重叠部分的面积为S,求S的最大值.
![](https://img.xkw.com/dksih/QBM/2015/7/9/1573868115787776/1573868122120192/STEM/54dbc9c564dd48c4a78fc2b44aaa2b27.png)
(1)是否存在点M,使△ABM为等腰三角形?若存在,分析点M的位置;若不存在,请说明理由;
(2)当点N在AD边上时,若BN⊥HN,NH交∠CDG的平分线于H,求证:BN=NH;
(3)过点M分别用AB、AD的垂线,垂足分别为E、F,矩形AEMF与△ACG重叠部分的面积为S,求S的最大值.
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【推荐2】抛物线y=ax2+bx+3(a≠0)经过点A(﹣1,0),B(
,0),且与y轴相交于点C.
(1)求这条抛物线的表达式;
(2)求∠ACB的度数;
(3)点D是抛物线上的一动点,是否存在点D,使得tan∠DCB=tan∠ACO.若存在,请求出点D的坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
(1)求这条抛物线的表达式;
(2)求∠ACB的度数;
(3)点D是抛物线上的一动点,是否存在点D,使得tan∠DCB=tan∠ACO.若存在,请求出点D的坐标,若不存在,说明理由.
![](https://img.xkw.com/dksih/QBM/2018/11/11/2073475753820160/2075192555413504/STEM/324321e972194ad78acaddccb16f9303.png?resizew=495)
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