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数学
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如图是一个抛物线拱桥的横截面,水面宽度AB为4米时,水面离拱桥的最大高度OC为2米.
(1)建立适当的坐标系求出抛物线的解析式;
(2)当水面下降1米时,水面的宽度相应增加多少米?
人气:138 ℃ 时间:2020-03-27 23:37:42
解答
(1)如图所示:设这条抛物线表示的二次函数为y=ax
2
,
由抛物线经过点(2,-2),
-2=4a
解得:a=-
1
2
,
所以,这条抛物线的二次函数为:y=-
1
2
x
2
,
(2)∵抛物线经过点(2,-2),
∴当水面下降1m时,水面的纵坐标为:y=-3,
-3=-
1
2
x
2
,
解得:x=±
6
,
所以,水面下降1m,水面的宽度为2
6
m,
∴水面的宽度增加了(2
6
-4)m.
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