图1是抛物线型拱桥,当水面在
时,拱顶离水面2米,水面宽4米,
(1)建立如下图2所示的直角坐标系,求抛物线的解析式.
(2)水面下降1米后,水面宽是多少?
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005935734784/1570005940797440/STEM/ff0e40cc6ad24299a2c861418c0c0da3.png?resizew=9)
(1)建立如下图2所示的直角坐标系,求抛物线的解析式.
(2)水面下降1米后,水面宽是多少?
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005935734784/1570005940797440/STEM/246a86c18b6246b1bf741a8d1c025fcc.png?resizew=344)
11-12高二上·湖南长沙·期末 查看更多[1]
(已下线)2011年湖南省长沙市铁路一中高二上学期期末检测数学文卷
更新时间:2016-11-30 14:08:10
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【知识点】 抛物线的应用
相似题推荐
解答题-问答题
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【推荐1】如图,斜率为1的直线过抛物线
的焦点,与抛物线交于两点A、B,将直线AB按向量
平移得直线
,N为
上的动点.
![](https://img.xkw.com/dksih/QBM/2011/5/12/1570192810598400/1570192815906816/STEM/5449d5d6d9c24bf2a2c8d6253dbb018d.png?resizew=151)
(1)若|AB|=8,求抛物线的方程;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4343313fca1c0be419110dca262ac998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/2011/5/12/1570192810598400/1570192815906816/STEM/5449d5d6d9c24bf2a2c8d6253dbb018d.png?resizew=151)
(1)若|AB|=8,求抛物线的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29b870cf6746c6956cf58be4e00ea58.png)
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【推荐2】已知抛物线
的焦点为F,直线
与抛物线C相切于点P,过点P作抛物线C的割线PQ,割线PQ与抛物线C的另一交点为Q,A为PQ的中点.过A作y轴的垂线与y轴交于点H,与直线l相交于点N,M为线段AN的中点.
(1)求抛物线C的方程;
(2)求证:点M在抛物线C上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06553b7e77205d053c1981e9c050d579.png)
(1)求抛物线C的方程;
(2)求证:点M在抛物线C上.
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【推荐3】用细钢管焊接而成的花坛围栏构件如图所示,它的外框是一个等腰梯形
,内部是一段抛物线和一根横梁.抛物线的顶点与梯形上底中点是焊接点
,梯形的腰紧靠在抛物线上,两条腰的中点是梯形的腰、抛物线以及横梁的焊接点
,
,抛物线与梯形下底的两个焊接点为
,
.已知梯形的高是40厘米,
、
两点间的距离为40厘米.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3825d421-276d-4d4a-a3ee-2a1b4948386f.png?resizew=166)
(1)以
为原点,梯形的上底所在直线为
轴,建立直角坐标系,求横梁
的长度;
(2)求梯形外框的用料长度.(注:细钢管的粗细等因素忽略不计,计算结果精确到1厘米.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134c3d2c318a33a82da4134dd17fa57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/3825d421-276d-4d4a-a3ee-2a1b4948386f.png?resizew=166)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求梯形外框的用料长度.(注:细钢管的粗细等因素忽略不计,计算结果精确到1厘米.)
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