如图,已知抛物线
与直线
的一个交点
在
轴上、另一交点为点
,直线
与
轴交于点
,抛物线的对称轴为直线
.交
轴于点
.
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712328892145664/2722084557520896/STEM/e33ae301-f452-4b8f-9093-ced5fb5a699c.png?resizew=235)
(1)求抛物线的解析式;
(2)点
是抛物线上
、
之间的一点,连接
、
,当
面积最小时,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e59da5115d0dafea24822245f92c48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.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/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712328892145664/2722084557520896/STEM/e33ae301-f452-4b8f-9093-ced5fb5a699c.png?resizew=235)
(1)求抛物线的解析式;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96645a3530e72d5d733d2c72147d340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
更新时间:2021-05-16 07:18:07
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相似题推荐
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适中
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【推荐1】已知抛物线的顶点(-1,-2)且图象经过(1,10),求此抛物线解析式.
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解答题-问答题
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【推荐2】如图1,在平面直角坐标系中,抛物线
与
轴分别交于
、
两点,与
轴交于点
,顶点为点
,连接
、
,点
为直线
上方抛物线上一动点,连接
交
于点
.
![](https://img.xkw.com/dksih/QBM/2022/6/9/2997715858391040/2998215270662144/STEM/12020c76065b4dc78ef9380e9ff9eec8.png?resizew=417)
(1)求抛物线的函数表达式及顶点
的坐标;
(2)当
的值最大时,求点
的坐标及
的最大值;
(3)如图2,在(2)的条件下,
是此抛物线对称轴上长为2的一条动线段(点
在点
上方),连接
、
,当四边形
周长取最小值时,求点
的坐标;在此条件下,以点
、
、
、
为顶点的四边形为平行四边形,直接写出点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90385c676848de67293e3ed6bc000fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbdef5d0c05acbf63fa72fa85c5bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc03fafb03395ed84030f03c5d93aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2022/6/9/2997715858391040/2998215270662144/STEM/12020c76065b4dc78ef9380e9ff9eec8.png?resizew=417)
(1)求抛物线的函数表达式及顶点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a6ce188523ed6ab24fa2bfa6e17fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a6ce188523ed6ab24fa2bfa6e17fdb.png)
(3)如图2,在(2)的条件下,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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适中
(0.65)
【推荐1】如图,函数y=-x2+bx+c的图象经过点A(m,0),B(0,n)两点,m,n分别是方程x2-2x-3=0的两个实数根,且m<n.
(1)求m,n的值以及函数的解析式;
(2)设抛物线y=-x2+bx+c与x轴的另一交点为点C,顶点为点D,连结BD、BC、CD,求△BDC面积;
(3)对于(1)中所求的函数y=-x2+bx+c,
①当0≤x≤3时,求函数y的最大值和最小值;
②设函数y在t≤x≤t+1内的最大值为p,最小值为q,若p-q=3,求t的值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/2cdc5b15-43d2-4ec3-b79a-43f27811e2ef.png?resizew=121)
(1)求m,n的值以及函数的解析式;
(2)设抛物线y=-x2+bx+c与x轴的另一交点为点C,顶点为点D,连结BD、BC、CD,求△BDC面积;
(3)对于(1)中所求的函数y=-x2+bx+c,
①当0≤x≤3时,求函数y的最大值和最小值;
②设函数y在t≤x≤t+1内的最大值为p,最小值为q,若p-q=3,求t的值.
您最近一年使用:0次
解答题-问答题
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适中
(0.65)
【推荐2】如图,在平面直角坐标系中,矩形OABC的顶点O为坐标原点,顶点A、C的坐标分别为(0,﹣
)、(2
,0),将矩形OABC绕点O顺时针旋转45°得到矩形OA′B′C′,边A′B′与y轴交于点D,经过坐标原点的抛物线y=ax2+bx同时经过点A′、C′.
(1)求抛物线所对应的函数表达式;
(2)写出点B′的坐标;
(3)点P是边OC′上一点,过点P作PQ⊥OC′,交抛物线位于y轴右侧部分于点Q,连接OQ、DQ,设△ODQ的面积为S,当直线PQ将矩形OA′B′C′的面积分为1:3的两部分时,求S的值;
(4)保持矩形OA′B′C′不动,将矩形OABC沿射线CO方向以每秒1个单位长度的速度平移,设平移时间为t秒(t>0).当矩形OABC与矩形OA′B′C′重叠部分图形为轴对称多边形时,直接写出t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求抛物线所对应的函数表达式;
(2)写出点B′的坐标;
(3)点P是边OC′上一点,过点P作PQ⊥OC′,交抛物线位于y轴右侧部分于点Q,连接OQ、DQ,设△ODQ的面积为S,当直线PQ将矩形OA′B′C′的面积分为1:3的两部分时,求S的值;
(4)保持矩形OA′B′C′不动,将矩形OABC沿射线CO方向以每秒1个单位长度的速度平移,设平移时间为t秒(t>0).当矩形OABC与矩形OA′B′C′重叠部分图形为轴对称多边形时,直接写出t的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/12/20/1633713970962432/1633713971429376/STEM/381683334e7c48d6b2a0ddbf305fb3ac.png)
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