题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094126-15790.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094127-31484.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094127-25588.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094127-21590.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094127-54099.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-53845.gif)
(1)求直线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-77248.gif)
(2)若点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-31952.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-77248.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-27385.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-18934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-86786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-33674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-53845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-18934.gif)
答案
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-47156.gif)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-62160.gif)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-43106.gif)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-17554.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-28590.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094127-54099.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-76288.gif)
设直线AC的解析式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094131-69829.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094127-54099.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094131-56941.gif)
直线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-77248.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-47156.gif)
(2)代数方法一:
过点D作DM∥y轴分别交线段AC和x轴于点M、N.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094131-19784.jpg)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094131-11102.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094132-68351.gif)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094132-90660.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094132-41629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094132-54613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094133-27448.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094133-18214.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094133-99751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-62160.gif)
代数方法二:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094133-41955.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094133-72150.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094134-15541.gif)
∴当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094133-99751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-62160.gif)
几何方法:
过点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-31952.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-77248.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094134-63439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094134-63439.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094134-87739.gif)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094134-27131.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094135-17539.gif)
当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094135-41584.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094134-63439.gif)
即:当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094135-94380.gif)
此时公共点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-31952.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094135-39492.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094136-58970.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094136-13314.gif)
=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-62160.gif)
即:当
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094133-99751.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-62160.gif)
(3)如图所示,由抛物线的轴对称性可求得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-53845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094136-26278.jpg)
∵以线段
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-86786.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-33674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-53845.gif)
∴过点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094128-53845.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-33674.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-18934.gif)
过点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094129-18934.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094136-82644.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094136-50470.gif)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094137-78439.gif)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094137-25750.gif)
∵B(1,0)
∴BE=1-x,PE=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094137-58024.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094137-97029.gif)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094138-92039.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094138-27854.gif)
∴P点的坐标为:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094130-43106.gif)
核心考点
试题【已知:抛物线,对称轴为直线,抛物线与y轴交于点,与轴交于、两点.(1)求直线的解析式;(2)若点是线段下方抛物线上的动点,求四边形面积的最大值;(3)为抛物线上】;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
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094118-78191.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094115-29726.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094111-70260.gif)
(1)将
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094111-70260.gif)
(2)指出该二次函数图象的对称轴和顶点坐标;
(3)当x取何值时,y随x的增大而增大?
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094105-81070.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019094106-50407.gif)
(1)求此二次函数的解析式;
(2)求此二次函数的图象与x轴的另一个交点的坐标;
(3)根据图象回答:当x取何值时,y<0?
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