龙凤湿地公园为大庆著名景点,该公园内圆形人工湖中心有一喷泉,在人工湖中央垂直于水面安装一个柱子,安置在柱子顶端的喷头向外喷水,水流在各个方向上沿形状相同的抛物线路径落下.爱思考的小东发现,如果设距喷水柱子的水平距离为米,喷出的抛物线形水线距离湖面高度为h米,h与
的数量变化有一定规律.
【提出问题】
喷出的抛物线形水线距离湖面高度为h米与距喷水的柱子的水平距离米,h与
之间有怎样的函数关系?
【分析问题】
小东对某个方向喷水的路径测量和计算得出如下数据:
| … | 0 | 1 | 2 | 3 | 4 | … |
h(米) | … | 2 | 2 | … |
(1)在建立如图1所示的平面直角坐标系,根据已知数据描点,并用平滑曲线连接;并直接写出h与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)现公园想通过喷泉设立一个新的游玩项目,使公园的平顶游船能从喷泉最高点的正下方通过.如果游船宽度为2.4米,顶棚到水面的高度为2米,为了避免游船被淋到,顶棚到水柱的垂直距离不小于0.8米,问游船在能否顺利通过?说明理由.
(3)如图2,若从安全的角度考虑,需要在这个喷泉外围设立一圈圆形护栏,这个喷泉的任何一条水柱在湖面上的落点到护栏的距离不能小于1m,请通过计算说明公园至少需要准备多少米的护栏?(结果保留
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
更新时间:2024-03-23 14:52:11
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解答题-问答题
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适中
(0.65)
【推荐1】已知二次函数
,当
时,
.
(1)求当
时,
的值;
(2)写出它的图像的开口方向,对称轴和顶点坐标;
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(1)求当
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(2)写出它的图像的开口方向,对称轴和顶点坐标;
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解答题-计算题
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适中
(0.65)
【推荐2】抛物线
的对称轴是直线
,且它的最低点在直线
上,求:
(1)函数解析式;
(2)若抛物线与
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轴交点为
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面积.
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解答题-问答题
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适中
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【推荐1】如图,抛物线
交
轴于A、
两点,交
轴于点
,点A坐标为
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为直径作
,
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(1)求抛物线的解析式;
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是
延长线上一点,
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交
于点
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的解析式;
(3)在(2)的条件下,抛物线上是否存在点P,使得
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(1)求抛物线的解析式;
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解答题-证明题
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适中
(0.65)
【推荐2】已知:如图1,在线段
的同侧作正方形
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