题目
题型:不详难度:来源:
二次函数
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-58962.gif)
(1)画出经过两次平移后所得到的图像,并写出函数的解析式.
(2)求经过两次平移后的图像与x轴的交点坐标,当x满足什么条件时,函数值大于0?
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-64043.gif)
(2)当x<
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-41884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-12899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095412-45230.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095412-26280.jpg)
依题意得:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095412-45230.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095412-98510.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-64043.gif)
∴平移后图像的解析式为:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-64043.gif)
(2)当y=0时,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-64043.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095412-42602.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095413-34332.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095413-62229.gif)
∴平移后的图像与x轴交与两点,坐标分别为(
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-41884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-12899.gif)
由图可知,当x<
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-41884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095411-12899.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095412-45230.gif)
核心考点
试题【(本小题满分11分)二次函数的图像如图8所示,请将此图像向右平移1个单位,再向下平移2个单位.(1)画出经过两次平移后所得到的图像,并写出函数的解析式.(2)求】;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/20191019/20191019095402-84336.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095402-45048.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095403-69336.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095403-81386.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095403-20043.gif)
(1)证明
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095403-52430.gif)
(2)若该函数图象的对称轴为直线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095403-46293.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095357-73684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095357-26765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095358-29815.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095353-80475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095353-41121.png)
① ac >0; ② a–b +c <0; ③当x <0时,y <0;
④方程
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095353-94163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095353-62202.png)
A.② ③ | B.② ④ | C.① ③ | D.① ④ |
在平面直角坐标系中,抛物线经过O(0,0)、A(4,0)、B(3,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095339-28773.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095339-68305.jpg)
(1)求此抛物线的解析式;
(2)以OA的中点M为圆心,OM长为半径作⊙M,在(1)中的抛物线上是否存在这样的点P,过点P作⊙M的切线l ,且l与x轴的夹角为30°,若存在,请求出此时点P的坐标;若不存在,请说明理由.(注意:本题中的结果可保留根号)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095318-66757.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095318-25938.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095318-43912.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095319-63919.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095319-46366.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095319-34285.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095319-58988.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095319-88297.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095320-97619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095320-41878.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095320-41861.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095320-91812.gif)
(2)判断
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095321-19537.gif)
(3)在线段
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095321-69008.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095321-92660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095321-96218.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095321-47260.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019095321-92660.gif)
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