题目内容
如图中是抛物线形拱桥,当水面在n时,拱顶离水面2m,水面宽4m,水面下降1m,水面宽度增加多少?![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103101545155412273/SYS201311031015451554122022_ST/images0.png)
【答案】分析:首先建立直角坐标系,设抛物线为y=ax2,把点(2,-2)代入求出解析式可解.
解答:解:如图,建立直角坐标,(1分)
可设这条抛物线为y=ax2,
把点(2,-2)代入,得
-2=a×22,a=
,
∴y=
,
当y=-3时,
.
∴水面下降1m,水面宽度增加(2
-4)m.
点评:本题考查点的坐标的求法及二次函数的实际应用.此题为数学建模题,借助二次函数解决实际问题.
解答:解:如图,建立直角坐标,(1分)
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103101545155412273/SYS201311031015451554122022_DA/images0.png)
把点(2,-2)代入,得
-2=a×22,a=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103101545155412273/SYS201311031015451554122022_DA/0.png)
∴y=
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103101545155412273/SYS201311031015451554122022_DA/1.png)
当y=-3时,
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103101545155412273/SYS201311031015451554122022_DA/2.png)
∴水面下降1m,水面宽度增加(2
![](http://thumb.1010pic.com/pic6/res/czsx/web/STSource/20131103101545155412273/SYS201311031015451554122022_DA/3.png)
点评:本题考查点的坐标的求法及二次函数的实际应用.此题为数学建模题,借助二次函数解决实际问题.
![](http://thumb2018.1010pic.com/images/loading.gif)
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