题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045707-81489.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045707-73582.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045707-14838.png)
(1)求该抛物线解析式并判断F点是否在该抛物线上;
(2)如图,动点P从点C出发,沿线段CB以每秒1个单位长度的速度向终点B运动;
同时,动点M从点A出发,沿线段AE以每秒
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045707-83464.png)
①问EP+PH+HF是否有最小值,如果有,求出t的值;如果没有,请说明理由.
②若△PMH是等腰三角形,求出此时t的值.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045707-51241.png)
还有(2)AN=t,MN=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-74180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-58026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-75873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-81617.png)
解析
试题分析:28、解:(1)y=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045707-51241.png)
(2)①∵E(0,6) ∴CE=CO
连接CF交x轴于H′,过H′作x轴的垂线交BC于P′,当P
运动到P′,当H运动到H′时, EP+PH+HF的值最小.
设直线CF的解析式为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045709-94510.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045709-95918.png)
∵C(0,3)、F(6,-3) ∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045709-30740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045709-85480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045709-92716.png)
当y=0时,x=3,∴H′(3,0) ∴CP=3 ∴t=3
②如图1,过M作MN⊥OA交OA于N
∵△AMN∽△AEO,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045710-88763.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045710-89407.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-74180.png)
Ⅰ.如图1,当PM=HM时,M在PH的垂直平分线上,
∴MN=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045710-44778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045710-98824.png)
Ⅱ.如图2,当PH=HM时,MH=3,MN=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-74180.png)
HN=OA-AN-OH=4-2t 在Rt△HMN中,
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045711-92412.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045711-61396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045711-15189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045711-91865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045711-30652.png)
Ⅲ.如图3.如图4,当PH=PM时,PM=3, MT=
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045712-70829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045712-72427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045712-61066.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045712-50006.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045713-14342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045713-60992.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045713-91710.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-58026.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-75873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045708-81617.png)
点评:本题难度较大,主要考查学生结合抛物线性质及矩形性质解决动点问题。动点问题为中考常考题型,注意培养数形结合思想,运用到考试中去。
核心考点
试题【如图(1),在平面直角坐标系中,矩形ABCO,B点坐标为(4,3),抛物线y=x2+bx+c经过矩形ABCO的顶点B、C,D为BC的中点,直线AD与y轴交于E点】;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/20191019/20191019045659-57989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045659-48698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045700-61928.png)
A.![]() |
B.当![]() |
C.![]() |
D.当![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045647-62297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045648-90971.png)
(1)求抛物线的解析式;
(2)将抛物线
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045647-62297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045648-80447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045648-80447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045648-12854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045648-71374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045648-12854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045649-65209.png)
①求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045649-54487.png)
②若点
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045649-38525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045648-12854.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045649-66329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045649-88867.png)
小丽:如果以10元/千克的价格销售,那么每天可售出300千克.
小强:如果每千克的利润为3元,那么每天可售出250千克.
小红:如果以13元/千克的价格销售,那么每天可获取利润750元.
【利润=(销售价-进价)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045644-25254.png)
(1)请根据他们的对话填写下表:
销售单价x(元/kg) | 10 | 11 | 13 |
销售量y(kg) | | | |
(3)设该超市销售这种水果每天获取的利润为W元,求W与x的函数关系式.当销售单价为何值时,每天可获得的利润最大?最大利润是多少元?
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045637-81336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045637-23757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045638-65607.png)
(1)填空:点C的坐标是 ,b= ,c= ;
(2)求线段QH的长(用含t的式子表示);
(3)依点P的变化,是否存在t的值,使以P、H、Q为顶点的三角形与△COQ相似?若存在,求出所有t的值;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-14511.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-87402.jpg)
(1)试求
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-14511.png)
(2)为了扩大销售量,公司决定拿出一定量的资金做广告,根据市场调查,若每年投入广告费为
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-12085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045632-33237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045632-33237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-12085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045632-39623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045632-33237.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-12085.png)
(3)在(2)的条件下求年利润S(万元)与广告费
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-12085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191019/20191019045631-12085.png)
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