1 . 如图1,在平面直角坐标系中,直线
与抛物线
交于
、
两点,其中
,
.该抛物线与
轴交于点
,与
轴交于另一点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/26/74bdd37e-64ff-4c9b-83b0-0fed98d62114.png?resizew=464)
(1)求
、
的值及该抛物线的解析式;
(2)如图2.若点
为线段
上的一动点(不与
、
重合).分别以
、
为斜边,在直线
的同侧作等腰直角
和等腰直角
,连接
,试确定
面积最大时
点的坐标.
(3)如图3.连接
、
,在线段
上是否存在点
,使得以
、
、
为顶点的三角形与
相似,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/9e6e15daf7b14dbff32c390f4984dcfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d88bbd34102b55fa928e8ff83f0d52.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/3d7a6fd6d651ae341154c2e40928d628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/906948588ab8a93adbacfd6606495fd0.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/26/74bdd37e-64ff-4c9b-83b0-0fed98d62114.png?resizew=464)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)如图2.若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/784b26de6134b6d3f5a81e2882a7d7f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfce6da93ad3e6053fe4d732f6e456b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3de0022a7f2e122492f1483e4d3cccba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)如图3.连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2 . 如图,四边形ABCD是梯形,
,抛物线过原点O,PC是抛物线的对称轴,且
.
(1)求抛物线的函数表达式;
(2)求点D的坐标;
(3)求直线AD的函数表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01271d4dd50c57eadadc5b174cf4cd19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e1d93b5a9750ad4b33d7a6acca4b4a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/1/b4040e3d-3dde-4dbf-8c42-30a05a2ee3b6.png?resizew=166)
(1)求抛物线的函数表达式;
(2)求点D的坐标;
(3)求直线AD的函数表达式.
您最近一年使用:0次
3 . 一次函数
的图象与x轴、y轴分别交于点A,B,点C是OA的中点,过点C作
于C,CD交一次函数图象于点D,P是OB上一动点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4de869ae6b6dc5b79fcae3de540b30bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/affbe2d2ced2303d8c3d183746d0bcf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186dee1a1cf68677d143172a2a50709c.png)
A.4 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-09-05更新
|
130次组卷
|
2卷引用:云南省昆明市第一中学2023-2024学年高一上学期入学考试数学试题
4 . 如图,△ABC是等腰直角三角形,∠ACB=90°,AC=BC,点P是△ABC内一点,连接PA,PB,PC,已知∠1=30°,∠2=∠3.
(1)求证:AP=BC;
(2)试探究△PAB与△PBC的面积的比值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/9eeddcfe-984c-44b9-96f3-60b7e3d65a36.png?resizew=214)
(1)求证:AP=BC;
(2)试探究△PAB与△PBC的面积的比值.
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