题目
题型:江苏中考真题难度:来源:
如图,在直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185607-78461.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185608-69353.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185608-16552.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185608-54964.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185609-26833.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185609-56372.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185609-58921.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185609-65671.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185609-82157.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185610-23510.gif)
(1)求证:点H为线段
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185610-42551.gif)
(2)求证:①四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185610-10909.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185610-54376.gif)
(3)除点P外,直线PH与抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185611-13503.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185611-83718.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185611-27491.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185611-73926.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185612-46373.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185612-68221.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185612-49924.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185612-12413.gif)
(2)①由(1)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185613-98215.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185613-40722.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185613-26828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185613-56046.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185613-48747.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185614-93707.gif)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185614-97734.gif)
∴四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185614-65055.gif)
②设
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185614-27641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185615-28718.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185615-43516.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185615-86995.gif)
过P作
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185615-35270.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185615-88480.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185616-13828.gif)
∴平行四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185616-81643.gif)
(3)设直线PR为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185616-47402.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185616-69500.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185616-63800.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185617-60912.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185617-12051.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185617-64710.gif)
∴直线PR为
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185617-15289.gif)
设直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185618-15555.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185618-48428.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185618-32781.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185618-79481.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185618-84801.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185619-91003.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185619-29406.gif)
所以直线PH与抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185619-87215.gif)
核心考点
试题【探索研究如图,在直角坐标系中,点P为函数在第一象限内的图象上的任一点,点A的坐标为,直线过且与x轴平行,过作y轴的平行线分别交x轴,于,连结交x轴于H,直线交y】;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/20191020/20191020185601-87133.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/20191020/20191020185601-27785.gif)
(2)在第(1)题的条件下,当直线l向左或向右平移时(包括l与直线BC重合),在直线AB上是否存在点P,使为等腰直角三角形?若存在,请直接写出所有满足条件的点P的坐标,若不存在,请说明理由。
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185543-69473.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185543-19273.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185543-26272.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185543-40151.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185544-46378.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185544-81198.gif)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185544-45656.gif)
(2)设抛物线的顶点为D,点P在抛物线的对称轴上,且
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185544-30465.gif)
(3)连结CD,求
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185545-68548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185545-52433.gif)
(1)求二次函数的解析式;
(2)写出二次函数图像的对称轴和顶点坐标。
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185522-82116.gif)
(Ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185523-21342.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185523-18389.gif)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185523-71776.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185523-17815.gif)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185523-57135.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185523-45937.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185524-29645.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185524-99807.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185524-87380.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185524-46462.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191020/20191020185515-71094.gif)
(1)求该二次函数的解析式;
(2)将该二次函数图象沿x轴向右平移几个单位,可使平移后所得图象经过坐标原点?并直接写出平移后所得图象与轴的另一个交点的坐标.
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