已知二次函数
的图象经过点
.
(1)求该二次函数的表达式.
(2)若该函数图象上的两点
,当
时,直接写出
的取值范围______.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab18968b35897a18615f6d0be695d610.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a2a5e336b6bcba6354fd366c892dd06.png)
(1)求该二次函数的表达式.
(2)若该函数图象上的两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188446added1c5104fd57fed7fbd97e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
更新时间:2023-12-17 22:38:51
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解答题-作图题
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【推荐1】某公园有一个小型喷泉,水柱从垂直于地面的喷水枪喷出,水柱落于地面的路径形状可以看作是抛物线的一部分.记喷出的水柱距喷水枪的水平距离为(单x位:m),距地面的垂直高度为y(单位:m),现测得x与y的几组对应数据如下:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/36480da3-920f-406b-9f60-18cc57d9e4bd.png?resizew=150)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/d528027d-9256-4985-adf3-96825bbc7aea.png?resizew=235)
请根据测得的数据,解决以下问题:
(1)在平面直角坐标系
中,描出以表中各组对应数据为坐标的点,并画出该函数的图象;
(2)结合表中所给数据或所画图象,得出水柱最高点距离地面的垂直高度为 m;
(3)求所画图象对应的二次函数表达式;
(4)公园准备在水柱下方的地面上竖直安装一根高
的石柱,使该喷水枪喷出的水柱恰好经过石柱顶端,则石柱距喷水枪的水平距离为 m.(注:不考虑石柱粗细等其他因素)
水平距离x/m | 0 | 1 | 2 | 3 | 4 | 5 | 6 | … |
垂直高度y/m | 0.7 | 1.6 | 2.3 | 2.8 | 3.1 | 3.2 | 3.1 | … |
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/36480da3-920f-406b-9f60-18cc57d9e4bd.png?resizew=150)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/d528027d-9256-4985-adf3-96825bbc7aea.png?resizew=235)
请根据测得的数据,解决以下问题:
(1)在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
(2)结合表中所给数据或所画图象,得出水柱最高点距离地面的垂直高度为 m;
(3)求所画图象对应的二次函数表达式;
(4)公园准备在水柱下方的地面上竖直安装一根高
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f31dae7586dbfef5de2b830bcbcffc.png)
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解答题-问答题
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【推荐2】在平面直角坐标系
中,直线l:
与抛物线
相交于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
.
(1)求该直线与抛物线的解析式;
(2)过点
作
∥
轴交抛物线于点
,设抛物线与
轴交于点
、
(点
在点
的左侧),求
的面积;
(3)点
(
,
)为
轴上一个动点,过点
作平行于
轴的直线与直线l和抛物线分别交于点
、
.当点
在点
上方时,求线段
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de0d508ab8a1cc3b503ac310d49cf06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d38c1b6daf7324ed7c282ea921b767.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d642138424be9ab9eef3c35172898589.png)
(1)求该直线与抛物线的解析式;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/81dea63b8ce3e51adf66cf7b9982a248.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://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/2021/1/30/2647227411800064/2651437235101696/STEM/3dd82e3a-d9d1-461e-b9fe-cff35d5f5141.png)
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【推荐1】一个二次函数图像上部分点的横坐标
,纵坐标
的对应值如下表:
(1)
的值为______;
(2)在给定的直角坐标系中,画出这个函数的图像;
(3)当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
… | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | … | |
… | 0 | 2 | 0 | -6 | … |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)在给定的直角坐标系中,画出这个函数的图像;
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b13d3854ea2671a9ae5be5b69a573e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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【推荐2】我们把函数图象上横坐标与纵坐标互为相反数的点定义为这个函数图象上的“互反点”.例如在二次函数
的图象上,存在一点
,则P为二次函数
图象上的“互反点”.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/7/585c1585-b446-4c8c-b67d-9a877dd6e7e4.png?resizew=480)
(1)分别判断
的图象上是否存在“互反点”?如果存在,求出“互反点”的坐标;如果不存在,说明理由.
(2)如图①,设函数
的图象上的“互反点”分别为点
过点B作
轴,垂足为C.当
的面积为5时,求b的值;
(3)如图②,
为x轴上的动点,过Q作直线
轴,若函数
的图象记为W1,将W1沿直线l翻折后的图象记为W2,当
两部分组成的图象上恰有2个“互反点”时,直接写出m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1fc8112feea4b0c9a6f94614df028c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344ccbf79da6ad7e3709d6fa72efb756.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/7/585c1585-b446-4c8c-b67d-9a877dd6e7e4.png?resizew=480)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e61457e9dfc1bc4bebba3fb8dd8e49b.png)
(2)如图①,设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59cf4fc91fde3bf793483aa5d2dc6abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e1704c0905ab7418c49fd279881e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b45db8dd8768994af51206565379fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)如图②,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ae5636e1348ee20d20ed37cbb4132c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165a501b2e6a3acc46212e59a166c053.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e178cfa70f09d6f4cc443e79bef51c.png)
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