已知二次函数
图象的一部分如图所示,它经过
.
(2)当
时,函数的最大值为
,最小值为
,若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e71461c5134339b5b54a80e588640f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b3c94d505e7c5bcce94afec4af3d92.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/416c41599a035e06d3b91bc30bfb715a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda1cf765ee5ba6a499ca0af78afe99f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
更新时间:2024-04-08 10:26:17
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【推荐1】“Water Slide”(水滑梯)是广泛深受人们欢迎的娱乐项目.如图所示,该设备电脑系统会根据游客的身体各项指标喷出适量的水流,以满足游客(看成一个点)在空中和水中的运动轨迹能形成如图所示的两段抛物线,以确保安全.
如图所示:游客在高速水流和重力的作用下,从C点脱离滑道,做抛物线运动,经过最高点D后,在点E处入水,入水后的运动轨迹仍然是抛物线,且与入水前的抛物线关于点E成中心对称,经过最低点F后在H处游出水面.已知
米,
轴,
米,
米,
轴,为节约用水,水池底部做成斜坡
,坡度
,
米,解答下列问题:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/10/d4efe96f-981b-4f86-b6f0-f334709edfb1.png?resizew=222)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/10/ce1e02ae-6c0c-4227-8b1e-1d7ab2d7c056.png?resizew=390)
(1)求入水后抛物线的解析式(即E点右侧的抛物线),不必写出自变量的取值范围.
(2)当游客与水池底部斜坡
的竖直距离超过0.7米时,不会发生危险.问:游客在此次入水的过程中是否会发生危险?请说明理由.
如图所示:游客在高速水流和重力的作用下,从C点脱离滑道,做抛物线运动,经过最高点D后,在点E处入水,入水后的运动轨迹仍然是抛物线,且与入水前的抛物线关于点E成中心对称,经过最低点F后在H处游出水面.已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f42f56b246c0eecf454c6ca8f956fb04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b5c50f862d14d11bae71261011cf97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a69b7672cd2925271115062a9863a6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d9258527e5b63ba9fda22701b7cafe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb7c47e3b286437d8e6ee8b7ec4f003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe36ef790f548a9d594c7b23e107dc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/10/d4efe96f-981b-4f86-b6f0-f334709edfb1.png?resizew=222)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/10/ce1e02ae-6c0c-4227-8b1e-1d7ab2d7c056.png?resizew=390)
(1)求入水后抛物线的解析式(即E点右侧的抛物线),不必写出自变量的取值范围.
(2)当游客与水池底部斜坡
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
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【推荐2】已知:如图,二次函数y=ax2+bx+c的图象与x轴交于A、B两点,其中A点坐标为(−1,0),B点坐标为(5,0)点C(0,5),M为它的顶点.
![](https://img.xkw.com/dksih/QBM/2019/10/14/2311942412574720/2315257832579072/STEM/14049c67f55f426db97253eaada557aa.png?resizew=153)
(1)求抛物线的解析式;
(2)求△MCB的面积.
![](https://img.xkw.com/dksih/QBM/2019/10/14/2311942412574720/2315257832579072/STEM/14049c67f55f426db97253eaada557aa.png?resizew=153)
(1)求抛物线的解析式;
(2)求△MCB的面积.
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解答题-证明题
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【推荐1】已知二次函数
的图象与
轴分别交于A、
两点(点A在点
的左边),以
为直径作
,
与
轴正半轴交于
,点
为劣弧
上一动点,连接
、
两弦相交于点
,连接
,
.
(1)求点
的坐标;
(2)若
的半径为3时,求
的值;
(3)请探索当点
运动到什么位置时,使得
与
相似,并给予证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d86667ae8cc7f37366f0c539cb189692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd6ffb78dad3375efa3b08ab518553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)请探索当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
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【推荐2】定义:对角线互相垂直且相等的四边形叫做垂等四边形.
中,已知四边形
是垂等四边形,点A的坐标为
,点C的坐标为
,则点B的坐标为 _______.
(2)综合探究:如图,已知抛物线
与x轴交于A,B两点,点A在点B的左侧,C,D两点在该抛物线上.若以A,B,C,D为顶点的四边形是垂等四边形.设点C的横坐标为m,点D的横坐标为n,且
,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132de9682ce9a412b7b517aa209726ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6001a48074a9870cea9688d824c9c8ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ddbf52f842281c506648a54ade4647.png)
(2)综合探究:如图,已知抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3236d825b994ee9c28e5d5479a57b8ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fc82bd80cb1c2b94498e59a4c8bc3e6.png)
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