设抛物线
与x轴交于点A(a,0) 和
.
(1)若
,求m、b的值;
(2)若
,求证:抛物线的顶点在直线
上;
(3)抛物线上有两点
和
,若
,试比较p 与q的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c1aa0ea7a4368ca62960d7eef0c2a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66d722922864a66102f255c51a14de7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde1051d1633f2782cf5d15dbd3a3262.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b0eb90cc26c4024df4980a882b696e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d71f4730e4c04ef4ec7ff3ca4d372c.png)
(3)抛物线上有两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49de8e5921f26dd5abd67a6f3bdb9f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd27f023a6e52a5df1c8e68d7be51e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201d17112773cbf1707b3cdf386e495a.png)
2017·浙江杭州·一模 查看更多[4]
浙江省杭州市拱墅区、滨江区、下城区2017年中考一模数学试卷2019年浙江省丽水市实验学校数学中考模拟试卷浙江省杭州市保俶塔实验学校2020-2021学年九年级上学期十月月考数学试题(已下线)【万唯原创】2021年陕西省试题研究-题组-重难题题组特训9-10
更新时间:2017-05-31 13:29:58
|
【知识点】 其他问题(二次函数综合)
相似题推荐
解答题-问答题
|
较难
(0.4)
【推荐1】如图①,抛物线
过点
,
,顶点为
.
(2)点
在第一象限的抛物线上,连接
,
,
,且
的面积为
.
①求点
的坐标;
②如图②,
是线段
上
与点
,
不重合
的动点,点
在
轴上,连接
,
,且
,求
的取值范围;
(3)若将线段
先向上平移
个单位长度,再向右平移
个单位长度,得到的线段与二次函数
的图象只有一个交点,其中
为常数,请直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d8de071a9c22c96a59b172d76c127e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d57173ef4cd72eb270686875dfd623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36488f7dff759ace2a27e56c3857056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](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/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147de24f071e316b68fd2e78e3c84545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af589a2bec9665af471acda5cec2d96.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②如图②,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ed2f8110b6431c50020303e5748abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ed04e08d287891ff58416cb460b3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若将线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa61b8d74454721b53384b7941a446d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解答题-问答题
|
较难
(0.4)
真题
【推荐2】如图,已知图①中抛物线
经过点D(-1,0),D(0,-1),E(1,0).
![](https://img.xkw.com/dksih/QBM/2015/7/14/1573871565324288/1573871571836928/STEM/978fc6f7-4fa3-4434-bae3-fcd7ad18797b.png)
(1)求图①中抛物线的函数表达式.
(2)将图①中的抛物线向上平移一个单位,得到图②中的抛物线,点D与点D1是平移前后的对应点,
求该抛物线的函数表达式.
(3)将图②中的抛物线绕原点O顺时针旋转90°后得到图③中的抛物线,所得到抛物线表达式为
,点D1与D2是旋转前后的对应点,求图③中抛物线的函数表达式.
(4)将图③中的抛物线绕原点O顺时针旋转90°后与直线
相交于A、B两点,D2与D3是旋转前后如图④,求线段AB的长.
![](https://img.xkw.com/dksih/QBM/2015/7/14/1573871565324288/1573871571836928/STEM/150f96c10dd54476a14fd0566fab33a0.png)
![](https://img.xkw.com/dksih/QBM/2015/7/14/1573871565324288/1573871571836928/STEM/978fc6f7-4fa3-4434-bae3-fcd7ad18797b.png)
(1)求图①中抛物线的函数表达式.
(2)将图①中的抛物线向上平移一个单位,得到图②中的抛物线,点D与点D1是平移前后的对应点,
求该抛物线的函数表达式.
(3)将图②中的抛物线绕原点O顺时针旋转90°后得到图③中的抛物线,所得到抛物线表达式为
![](https://img.xkw.com/dksih/QBM/2015/7/14/1573871565324288/1573871571836928/STEM/d278484419f64f5383b5c59a15fc8962.png)
(4)将图③中的抛物线绕原点O顺时针旋转90°后与直线
![](https://img.xkw.com/dksih/QBM/2015/7/14/1573871565324288/1573871571836928/STEM/c19fb359f4014099be43df8100bf2c43.png)
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解答题-问答题
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较难
(0.4)
【推荐3】如图1,抛物线
与x轴交于点A,B(A在B左边),与y轴交于点C,连
,点D与点C关于抛物线的对称轴对称,过点D作
交抛物线于点E,交y轴于点P.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/9ed640cf-cfc8-4617-ad94-a4c50c1d83cd.png?resizew=574)
(1)点F是直线
下方抛物线上点一动点,连
交
于点G,连
,当
的面积的最大值时,直线
上有一动点M,直线
上有一动点N,满足
,连
,
,求
的最小值;
(2)如图2,在(1)的条件下,过点F作
轴于点H交
于点L,将
沿着射线
平移到点A与点C重合,从而得到
(点A,H,L分别对应点
,
,
),再将
绕点
逆时针旋转
,旋转过程中,边
所在直线交直线
于Q,交y轴于点R,求当
为等腰三角形时,直接写出
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067c1757833b8d5baf2c621c8e8f0767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105068b25f5a63af32f4082cfe08691e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/17/9ed640cf-cfc8-4617-ad94-a4c50c1d83cd.png?resizew=574)
(1)点F是直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e5e61804ce550636a0354e0a78a22d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66fae8e33cd86fa8dab72704eaafe1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9e953a4a5f98c96bbe67cbaadf76d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5dbfcff5c8b5d4e312a9247b2b8b0a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73aa23916dd546c43e96c8e5394e729e.png)
(2)如图2,在(1)的条件下,过点F作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ecb6778c97278d3d6ed32154448425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b629abf0700e3b7cc728f1081cfa54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f1bca1ca677b523e4a466842b3bc20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d955d197e2ecbfe724570663efcf2a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf90af48c665ee801c05cc55914b8fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44f1bca1ca677b523e4a466842b3bc20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d955d197e2ecbfe724570663efcf2a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0c6b3ac303e83e204a619ac3d5e1bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d1ecab5768cc431b5e45ad256042d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f97913e1af1e6c793f7edfe6b2114.png)
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