二次函数
.
(1)当
时,函数图象与x轴交于点A、B,与y轴交于点C.
①直接写出函数的解析式;
②如图1,点P是第四象限内函数图象上一动点,求出点P坐标,使得
的面积最大;
③如图2,在抛物线上是否存在点Q,使
,若存在请求出点Q的坐标;若不存在,请说明理由;
(2)点
、
为函数图象上任意两点,且
.若对于
时,都有
,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d51c74942a8d26cc180cc34315e406.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/f2c15b83-c6d7-4cdf-b6ec-98abcb905218.png?resizew=238)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
①直接写出函数的解析式;
②如图1,点P是第四象限内函数图象上一动点,求出点P坐标,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
③如图2,在抛物线上是否存在点Q,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f3ca1088f1455db5c1194ba484b224.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c556b35e2216aeb5b7d8b1b4c140da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac67e9a909472ab852d38d2ec66a1e1.png)
更新时间:2023-11-03 16:18:02
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相似题推荐
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【推荐1】在平面直角坐标系中,抛物线
(
为常数)经过点
,点A在抛物线上,其横坐标为
,将此抛物线上
两点间的部分(包括
两点)记为图象
.
(1)求此抛物线的解析式.
(2)当
垂直于
轴时,求
的值.
(3)当图像
与直线
有且只有一个交点时,求
的取值范围.
(4)已知点
,顺次连结
得到矩形
,当图象
与该矩形的边有且只有两个公共点时,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c1be55ce3ff86ba89cb1c84dc88ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b07bddd9bebc06909947a3f429ce3348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76058a23db1e02787bbeab9ee57fc7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)求此抛物线的解析式.
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当图像
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b488f2e232b6e30359d39347c9e23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(4)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e26e851bb4b71e1d48c8d566b92f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29edbf401289f766bc5c760a9fce5090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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【推荐2】如图,在抛物线
与x轴交于点A,B,与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/1034a8a4-48b7-4bf9-b3b0-e7c917fc8086.png?resizew=144)
(1)若点A的坐标为
,求抛物线的解析式及顶点坐标;
(2)在(1)的条件下,设点
为抛物线上一点,当
时,点P的纵坐标y满足
,求
的值;
(3)已知平面直角坐标系中的点
,
,连接
,若抛物线与线段
只有一个公共点,观察函数图象,请直接写出c的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0a689a0bea86ac5512d89d2fb8f73d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/11/1034a8a4-48b7-4bf9-b3b0-e7c917fc8086.png?resizew=144)
(1)若点A的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
(2)在(1)的条件下,设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e71bfb1e9378d7ebe58bb41899434615.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d30ef282faeb29715cc49d5e8fff130a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
(3)已知平面直角坐标系中的点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d479940147c1ff18724a453ba8587b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fc37d9845dc0e11a1e69e3f1857785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
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【推荐3】【问题背景】
水火箭是一种基于水和压缩空气的简易火箭,通常由塑胶汽水瓶作为火箭的箭身,并把水当作喷射剂.图1是某学校兴趣小组制做出的一款简易弹射水火箭.
为验证水火箭的一些性能,兴趣小组同学通过测试收集了水火箭相对于出发点的水平距离
(单位:
)与飞行时间
(单位:
)的数据,并确定了函数表达式为:
.同时也收集了飞行高度
(单位:
)与飞行时间
(单位:
)的数据,发现其近似满足二次函数关系.数据如表所示:
【建立模型】
任务1:求
关于
的函数表达式.
【反思优化】
图2是兴趣小组同学在室内操场的水平地面上设置一个高度可以变化的发射平台(距离地面的高度为
),当弹射高度变化时,水火箭飞行的轨迹可视为抛物线上下平移得到,线段
为水火箭回收区域,已知
,
.
任务2:探究飞行距离,当水火箭落地(高度为
)时,求水火箭飞行的水平距离.
任务3:当水火箭落到
内(包括端点
,
),求发射台高度
的取值范围.
水火箭是一种基于水和压缩空气的简易火箭,通常由塑胶汽水瓶作为火箭的箭身,并把水当作喷射剂.图1是某学校兴趣小组制做出的一款简易弹射水火箭.
为验证水火箭的一些性能,兴趣小组同学通过测试收集了水火箭相对于出发点的水平距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65502a7ea4d1ce6d6d8c720845c73e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241c155e0733b9751070944b1a695226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65502a7ea4d1ce6d6d8c720845c73e0.png)
飞行时间 | 0 | 2 | 4 | 6 | 8 | … |
飞行高度 | 0 | 10 | 16 | 18 | 16 | … |
任务1:求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
【反思优化】
图2是兴趣小组同学在室内操场的水平地面上设置一个高度可以变化的发射平台(距离地面的高度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1098e4a574a43a1768884606034a68a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8e9547963034edc53639045b5aed67.png)
任务2:探究飞行距离,当水火箭落地(高度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0169849639a13aff719bd2959ddfb760.png)
任务3:当水火箭落到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/7a5f1641947153c80b987320885a2b57.png)
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【推荐1】如图,二次函数y=2mx2+5mx﹣12m(m为参数,且m<0)的图象与x轴交于点A、B,与y轴交于点C,点A的坐标为(﹣4,0).
(1)求直线AC的解析式(用含m的式子表示).
(2)若m=﹣
,连接BC,判断∠CAB和∠CBA的数量关系,并说明理由.
(3)在(2)的条件下,设点M为AC上方的抛物线上一动点(与点A,C不重合),以M为圆心的圆与直线AC相切,求⊙M面积的取值范围.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/20/676be8c7-0777-48d7-b091-6f5b70914028.png?resizew=395)
(1)求直线AC的解析式(用含m的式子表示).
(2)若m=﹣
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
(3)在(2)的条件下,设点M为AC上方的抛物线上一动点(与点A,C不重合),以M为圆心的圆与直线AC相切,求⊙M面积的取值范围.
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【推荐2】如图,点
,
,线段
与
轴平行,且
,点
在点
的右侧,抛物线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/173e1892-868b-4482-b41b-dc169eb3b783.png?resizew=179)
(1)①该抛物线的对称轴为___________;
②当
时,求
的最大值(用含
的代数式表示).
(2)当抛物线
经过点
时
①点
___________(填“是”或“不”)在
上;
②连接
,点
是第一象限内抛物线上的动点,设点
的横坐标为
,过点
作
,垂足为点
,则
时,
___________.
(3)在(2)的条件下,若线段
以每秒2个单位长的速度向下平移,设平移的时间为
(秒)
①若
与线段
总有公共点,求
的取值范围;
②若
同时以每秒3个单位长的速度向下平移,
在
轴及其右侧的图象与直线
总有两个公共点,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc979751c084c666d9f838dea6ef151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced6f5181811d441997b2ff1cd35a73e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/19/173e1892-868b-4482-b41b-dc169eb3b783.png?resizew=179)
(1)①该抛物线的对称轴为___________;
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836d745b71ec18b1135e8bbf6990bffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c052d7af2f98d95bac8725b608fba0fc.png)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829fc6685b59fdc609f32f30ebd9e6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b092934ebc48422434232d474cb7c9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
(3)在(2)的条件下,若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②若
![](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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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【推荐3】已知抛物线
与
轴交于点
,它的顶点为点
,点
,
关于原点
的对称点分别为
,
,若
,
,
,
中任何三点都不在一条直线上,则称四边形
为抛物线的伴随四边形,直线
为抛物线的伴随直线.
(1)如图(
)所示,求抛物线
的伴随直线的解析式;
(2)如图(
)所示,若抛物线
的伴随直线是
,且顶点横坐标为
.求此抛物线的解析式;
(3)如图(
)所示,若抛物线
的伴随直线是
,且伴随四边形
是矩形.
求
,
的值
在抛物线的对称轴上是否存在点
,使得
是一个等腰三角形?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/36616e005dbf8ccfbda50a31115df7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/3/e8310252-ba7f-4da6-bcb0-addc0956b58a.png?resizew=372)
(1)如图(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/546130969019c93e7e87be2773760a8e.png)
(2)如图(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36616e005dbf8ccfbda50a31115df7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e235d7dd12f948f5ffb2e5afddc95612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(3)如图(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36616e005dbf8ccfbda50a31115df7ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40da46314ca911fcf7347648cc63afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1c9ae241fd78126274c65e17990c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c650fe55b7603f106c53ca2423451c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acee03d4bb4667b6c345221b6c9b0fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐1】如图,在平面直角坐标系中,抛物线
与
轴交于两点:
,与
轴交于点
.点
分别是
上的动点,当点
从
点出发,在线段
上以每秒3个单位长度的速度向
点运动,同时点
从
点出发,在线段
上以每秒1个单位长度的速度向
点运动,其中一个点到达终点时,另一个点也停止运动.设
同时运动的时间为
秒
.
(2)设
的面积为
,当
为何值时,
的面积最大,最大面积是多少?
(3)当
为何值时,
是以
为腰的等腰三角形?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78531ca6d555e824f53ebae6adb666a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce34778c6f08368c6d2c66ed1a9b8e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3355e2fa0ac6c675f02ee36c3ced4f2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/108d2e71cac3fa2dc106a193c56c5320.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c495b8fd7f7bb21c177c9d50fbf6919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c495b8fd7f7bb21c177c9d50fbf6919.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c495b8fd7f7bb21c177c9d50fbf6919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
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名校
【推荐2】如图1,已知二次函数
(a、b、c为常数,且
)的图象,与x轴交于A、B两点(A点在B点左侧),与y轴交于点
,且其函数表达式可以变形为
的形式.已知点P为该抛物线在第一象限内的一动点,设其横坐标为m.
(2)连接
,过点
作
轴于点
,交
于点
,直线
交
轴于点
,连接
.
①求出直线
的函数表达式(用含有
的代数式表示);
②设四边形
的面积为
,求
关于
的函数关系式,并求
的最大值;
(3)如图2,若直线
为该二次函数图象的对称轴,交
轴于点
,直线
,
分别交直线
于点
、
.在点
运动的过程中,
是否为定值?若是,请求出该定值;若不是,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/c052d7af2f98d95bac8725b608fba0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d89057bac47a9d19b74b34a5fffd9d9.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2784a52c4da98dc9df661fc152fc29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
①求出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②设四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62d0314d180fa3cc2dfee87a3c22adf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(3)如图2,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f000eef0716f7bf5c49d6d17b4467a.png)
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【推荐1】如图,二次函数
的图象与x轴交于A、B两点(点A在点B的右侧),与y轴交于点C.
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952388087947264/2957785547964416/STEM/3c8c8571-7a7e-4238-9ca9-76070553dacb.png?resizew=189)
(1)求点A、B、C的坐标;
(2)若点M在抛物线的对称轴上,且△MAC的周长最小,求点M的坐标;
(3)若点P在x轴上,且△PBC为等腰三角形,请求出所有符合条件的点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a707e2d3361739d358880e76443167.png)
![](https://img.xkw.com/dksih/QBM/2022/4/6/2952388087947264/2957785547964416/STEM/3c8c8571-7a7e-4238-9ca9-76070553dacb.png?resizew=189)
(1)求点A、B、C的坐标;
(2)若点M在抛物线的对称轴上,且△MAC的周长最小,求点M的坐标;
(3)若点P在x轴上,且△PBC为等腰三角形,请求出所有符合条件的点P的坐标.
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【推荐2】已知抛物线
与
轴相交于点
,
,且
,
是方程
的两个实数根,点C为抛物线与y轴的交点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/a7e5a635-989e-4662-b34a-6b1e7e4b422b.png?resizew=253)
(1)求a,b的值;
(2)分别求出直线
和
的解析式;
(3)若动直线
与线段
,
分别相交于D,E两点,则在x轴上是否存在点P,使得
为等腰直角三角形?若存在,求出点P的坐标:若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0d44326c214c7a5ecc3068a29ec96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ec3d75e53b990bc8f9a4622928dd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ae7486a9ecc9fa47de8b07cbee9677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8034dddd265a186e29172623e3b9eadf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/a7e5a635-989e-4662-b34a-6b1e7e4b422b.png?resizew=253)
(1)求a,b的值;
(2)分别求出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)若动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ee8b6d5526632161e70ac159d6c96a.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/a4336efb6d0689ddad55295e336340d3.png)
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