题目
题型:同步题难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190803-91467.gif)
(2)如图2,若AE上有一动点P(不与A,E重合)自A点沿AE方向向E点匀速运动,运动的速度为每秒1个单位长度,设运动的时间为t秒(
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190804-76833.gif)
(3)在(2)的条件下,当t为何值时,以A,M,E为顶点的三角形为等腰三角形,并求出相应的时刻点M的坐标。
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190804-13960.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190804-56201.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190804-43868.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190804-99607.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190805-59599.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190805-21740.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190805-37309.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190805-70986.gif)
解得:
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190805-83730.gif)
∴D点坐标为(0,
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190806-45698.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190806-35072.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190806-45176.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190806-74595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190807-96712.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190807-26269.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190807-13126.gif)
而显然四边形为矩形,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190807-35317.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190808-16308.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190808-17613.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190808-11507.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190808-60327.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190809-20287.gif)
(3)(i)若以AE为等腰三角形的底,则
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190809-79623.gif)
如图1,
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190810-50342.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190810-96934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190810-12146.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190811-98022.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190811-15583.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190811-13364.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190811-89490.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190812-82416.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190812-17325.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190812-45692.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190812-26285.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190813-16932.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190813-95291.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190813-38025.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190813-44242.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190814-66277.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190814-21755.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190814-79940.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190814-91349.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190814-56932.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190815-54536.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190815-88061.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190815-73201.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190815-57662.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190815-23379.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190816-79510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190816-65276.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190816-24886.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190816-39838.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190817-75563.gif)
相应点的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190817-94510.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190817-80180.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190817-72497.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190817-96656.gif)
核心考点
试题【如图1,OABC是一张放在平面直角坐标系中的矩形纸片,O为原点,点A在x轴的正半轴上,点C在y轴的正半轴上,OA=5,OC=4。(1)在OC边上取一点D,将纸片】;主要考察你对二次函数的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190758-29066.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190758-19846.gif)
(1)求证:4p+5q=0;
(2)问是否存在一个圆O′,经过A、B两点,且与y轴相切于C点,若存在试确定此时抛物线的解析式及圆心O′的坐标,若不存在,请说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190753-95324.gif)
(2)请预测未来40天中那一天的销售利润最大,最大日销售利润是多少?
(3)在实际销售的前20天中该公司决定每销售一件商品就捐赠a 元利润(a<4)给希望工程,公司通过销售记录发现,前20 天中,每天扣除捐赠后的日销售利润随时间t的增大而增大, 求a的取值范围。
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190747-78553.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190747-47721.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190747-63312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190747-72168.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190748-53786.gif)
①求梯形上底AB的长及直角梯形OABC的面积;
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190748-50673.gif)
(2)在第(1)题的条件下,当直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190748-38464.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190748-68895.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190749-20882.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190738-50506.gif)
①AD边的长度如何表示?
②当x取何值时,矩形铁皮的面积最大?最大值是多少?
(2)小亮建议利用图②的分割方法,他认为能裁出面积更大的矩形铁皮,你认为他的想法能否实现?为什么?
(1)求过A,B,C三点的抛物线的解析式;
(2)求出该抛物线的对称轴和顶点坐标;
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020190734-45394.gif)
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