题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045839-47524.png)
(1)求抛物线的解析式;
(2)已知点D(m,m+1)在第一象限的抛物线上,求点D关于直线BC对称的点的坐标;
(3)在(2)的条件下,连接BD,点P为抛物线上一点,且∠DBP=45°,求点P的坐标.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-99201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-82333.png)
解析
试题分析:.解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-26399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-72742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-96684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-51330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-85684.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-39096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-46291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-99201.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-26618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-73146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-85129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-88384.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-17522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-67365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-81368.png)
在D第一象限,点D的坐标为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-91017.png)
由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045841-53648.png)
设点D关于直线BC的对称点为点E.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045842-20961.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045842-65752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045842-61444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045842-21218.png)
E点在Y轴上,且
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045842-30295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045842-34870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-85028.png)
即点D关于直线BC对称的点的坐标为(0,1). 7分
(3)方法一:作
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-96540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-16492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-96087.png)
由(1)有:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-23497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-92257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-43612.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-22699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045843-74590.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-60011.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-85441.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-71275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-11342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-71126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-10371.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-47634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-87744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045844-73518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-32763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-76128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-46291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-81040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-90128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-57497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-72058.png)
(其它方法参照以上标准给分)
方法二:过点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-43776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045845-68458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045846-37811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045846-95221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045846-79677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045846-58107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045846-30091.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045846-64706.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045846-54648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-36584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-60793.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-68145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-28841.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-94406.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-80845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-93432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-54417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045847-66286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045848-64708.png)
由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045848-55760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045848-37412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045848-65079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045848-93394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045848-25156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045848-38597.png)
解方程组
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045849-26158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045849-91285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045849-19638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045849-16286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045849-48782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045840-82333.png)
点评:解答本题的的关键是熟练掌握有两组角对应相等的两个三角形相似;两组边对应成比例且夹角相等的三角形相似.
核心考点
试题【如图,抛物线y=ax2+bx-4a经过A(-1,0)、C(0,4)两点,与x轴交于另一点B.(1)求抛物线的解析式;(2)已知点D(m,m+1)在第一象限的抛物】;主要考察你对二次函数定义等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045831-33090.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045831-68871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045831-37022.png)
(1)求抛物线的解析式;
(2)设点D的横坐标为m,则用m的代数式表示线段DC的长;
(3)在(2)的条件下,若△ADB的面积为S,求S关于m的函数关系式,并求出当S取最大值时的点C的坐标;
(4)当点D为抛物线的顶点时,若点P是抛物线上的动点,点Q是直线AB上的动点,判断有几个位置能使以点P,Q,C,D为顶点的四边形为平行四边形,直接写出相应的点Q的坐标.
① 当m=-1时,函数图象的顶点坐标是(1,0);
② 当m>0时,函数图象截x轴所得的线段长度大于1;
③ 当m<0时,函数在x>
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045823-79142.png)
④ 不论m取何值,函数图象经过一个定点.
其中正确的结论有 ( )
A.4个 | B.3个 | C.2个 | D.1个 |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045820-95388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045820-49360.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045820-55955.png)
商品名称 金 额 | A | B | |||
投资金额x(万元) | x | 5 | x | 1 | 5 |
销售收入y(万元) | y1=kx (k≠0) | 3 | y2=ax2+bx(a≠0) | 2.8 | 10 |
(2)为满足市场需求,商店准备投资20万元同时购进A、B两种新黄金产品。其中购买A、B两种新黄金产品所投资的金额与销售收入存在如图所示的函数对应关系. 请你判断商店这次投资能否盈利?
(3)在(2)的其他条件不变的情况下,商店准备投资m万元同时购进A、B两种新黄金产品,并实现最大盈利3.2万元,请求出m的值.(利润=销售收入-投资金额)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045813-46177.png)
(1)求该抛物线的解析式及顶点D坐标;
(2)如图,若P为线段CD上的一个动点,过点P作PM⊥x轴于点M,求四边形PMAB的面积的最大值和此时点P的坐标;
(3)过抛物线顶点D,作DE⊥x轴于E点,F(m,0)是x轴上一动点,若以BF为直径的圆与线段DE有公共点,求m的取值范围.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045809-66510.png)
(1)填空:A点坐标为(____,____),D点坐标为(____,____);
(2)若抛物线y=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045810-55824.png)
(3)将(2)中的抛物线沿y轴向上平移,设平移后所得抛物线与y轴交点为E,点M是平移后的抛物线与直线AB的公共点,在抛物线平移过程中是否存在某一位置使得直线EM∥x轴.若存在,此时抛物线向上平移了几个单位?若不存在,请说明理由.
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