题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062552-45270.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062552-96361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062552-93728.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062552-46262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-95296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-42721.png)
(1)求这个二次函数的解析式及顶点坐标;
(2)在
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-20398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-99830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-99830.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-59361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-91773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-99830.png)
(3)在(2)的条件下,将
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-75769.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-75173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-80754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-49447.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-65535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-26631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-49035.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-89451.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-67838.png)
所以这个二次函数的解析式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-65535.png)
顶点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062553-95296.png)
解:(2)【解法一】设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-31295.png)
由题意,得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-81513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062555-67852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062555-79929.png)
1分
∵∠APD=90°,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062555-68261.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062555-72235.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062555-29170.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-26631.png)
【解法二】如图,作
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062556-95060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062556-49809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062556-61453.png)
则由题意,得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062556-22047.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062556-44431.png)
由∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062557-96723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062557-18408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062557-38160.png)
由∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062557-42986.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062557-18408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062558-13704.png)
∴∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062558-70882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062558-53384.png)
又∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062557-18408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062558-13535.png)
∴△
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062558-70882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062558-53384.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062559-30243.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062559-45158.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062559-79304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062559-95417.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-26631.png)
解:(3)【解法一】如图,作
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062559-25912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062600-28752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062600-60953.png)
易得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062600-42544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062600-67787.png)
∴四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062601-50404.png)
由∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062601-10382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062601-89082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062601-31917.png)
由∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062602-68234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062557-18408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062601-31917.png)
∴∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062602-69012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062601-89082.png)
又∠
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062602-90179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062602-40470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062602-88182.png)
∴△
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062602-90179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062603-85240.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062603-80279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062603-49635.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-49035.png)
【解法二】]设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062603-97287.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062603-24710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062604-46359.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062604-15695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062604-52871.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062554-49035.png)
(1)将A、B、C三点坐标代入y=ax2+bx+c中,列方程组求a、b、c的值,得出二次函数解析式,根据顶点坐标公式求顶点坐标;
(2)设P(0,m),由勾股定理分别表示PA,PD,AD的长,由于∠APD=90°,在Rt△PAD中,由勾股定理列方程求m的值即可;
(3)作QH⊥x轴,垂足为点H,由勾股定理求出PA=PD=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062604-79345.png)
核心考点
试题【如图,在平面直角坐标系中,二次函数的图像经过点,,,顶点为.(1)求这个二次函数的解析式及顶点坐标;(2)在轴上找一点(点与点不重合),使得,求点坐标;(3)在】;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/20191019/20191019062538-40596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-79948.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-38451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-75460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-25644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-38451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-67140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-75460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-78554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-62139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-76696.jpg)
(1)求点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062538-67140.png)
(2)如果
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062539-50337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062525-90362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062525-10644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062525-68901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062525-96786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062526-64881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062526-35016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062526-69583.png)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062526-64881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062526-19663.png)
(2)点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062527-87786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062527-18212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062526-35016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062527-88955.png)
(3)以
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062527-66846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062527-51674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062526-19663.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062528-35695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062527-51674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062512-17157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062512-66370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062512-17157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062513-29752.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062513-98057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062513-45065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062513-48991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062514-88232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062512-17157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062514-83392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062514-71650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062514-48628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062514-46739.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062515-70735.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062515-35957.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062515-95649.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062515-21625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062516-88105.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062516-28744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062501-56081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062501-23033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062501-68739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-56520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-44540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-96497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-56520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-44540.png)
(1)求该抛物线的表达式,并写出该抛物线的对称轴和顶点坐标;
(2)记该抛物线的对称轴为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-41611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-44540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062502-41611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062503-53457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062503-22730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062501-68739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062503-15776.png)
① 求点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062503-22730.png)
② 将此抛物线向右平移,平移后抛物线的顶点为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062503-16386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062501-56081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062503-94683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062504-24455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062504-21233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062504-20445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062504-66482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062440-75720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062441-76685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062441-30884.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062441-84482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062441-74831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062442-89784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062441-74831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062442-22113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062442-32473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062442-26642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062443-27641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062443-83551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062443-69922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062443-17951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062443-62273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062444-35139.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062442-26642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062444-24415.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062444-83477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062444-28045.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062445-65465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062440-75720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062445-30380.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062445-16837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062440-75720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062445-78773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062446-33737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062446-33737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062446-32998.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062446-32998.png)
(3)如果
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062440-75720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062445-78773.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062446-96093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062446-56122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019062446-59383.png)
最新试题
- 1公民参与管理国家和管理社会的基础和标志是 A.行使选举和被选举权B.行使政治自由C.行使监督权 D.行使知情权
- 2如图所示,在细绳的O处用水平力F缓慢拉起重物,在此过程中,绳的拉力F1和水平力F2的变化情况是( )A.F1、F2都
- 3中国近代最早的外交机构是( )A.军机处B.户部C.吏部D.总理衙门
- 4下列关于点电荷的说法正确的是A.点电荷的带电量必须很少B.带电体体积较大时一定不能看成是点电荷C.点电荷所带电荷量可能是
- 5计算:︱-5︱=_____________.
- 6读“地壳物质循环简图”,完成1—2题。1、图示a、b、c、d岩石中,属于沉积岩的是[ ]A、a B、b
- 7“ Frank , how far is it from your home to school ? ” “ It "
- 8下列城市中,既是近代中国最早开放的通商口岸,又是第一批开放的经济特区是()A.深圳B.珠海C.广州D.厦门
- 9植物果实和种子的传播方式有______、______、______和______等方式,这样就扩大了植物的生活范围.
- 101995年,***江泽民发表《为促进祖国统一大业的完成而继续奋斗》的重要讲话,强调祖国和平统一的基础和前提是[
热门考点
- 1设常数a>0, 展开式中x3的系数为, 则____.
- 2本小题满分12分)已知,,,且,,求点及向量的坐标.
- 3设函数在区间(0,4)上是减函数,则k的取值范围是[ ]A. B. C.
- 4Dr Watson wrote his name and carefully at the top of the
- 5听句子,选择正确答语。( ) 1. A. Sure. ( ) 2. A. I"m wa
- 6氯化钠是生活必需品,也是重要的化工原料。提纯含少量泥沙的粗盐,一般经过下列操作流程:(1)操作④中必须用到的一种仪器是_
- 7化简x2+5xx-1-2x2+4xx2-x的结果是______.
- 8小明同学在一只矿泉水瓶内装入密度为ρ的某种液体,液面距瓶底高H,求在距瓶底H处液体产生的压强是多少?(计算结果用字母表示
- 9曹操《短歌行》“山不厌高, 。 , 。”表达了曹操尽可能多地接纳贤才
- 10阅读下列材料,回答问题。材料一:第一次世界大战后,战胜的协约国集团为了缔结和约,对战后的世界做出安排,召开巴黎和会。操纵