某数学兴趣小组运用《几何画板》软件探究y=ax2(a>0)型抛物线图象.发现:如图1所示,该类型图象上任意一点M到定点 F(0,
)的距离MF,始终等于它到定直线l:y=﹣
上的距离MN(该结论不需要证明),他们称:定点F为图象的焦点,定直线l为图象的准线,y=﹣
叫做抛物线的准线方程.其中原点O为FH的中点,FH=2OF=
,例如,抛物线y=
x2,其焦点坐标为F(0,
),准线方程为l:y=﹣
.其中MF=MN,FH=2OH=1.
请分别直接写出抛物线y=2x2的焦点坐标和准线l的方程: , .
(2)【技能训练】
如图2所示,已知抛物线y=
x2上一点P到准线l的距离为6,求点P的坐标;
(3)【能力提升】
如图3所示,已知过抛物线y=ax2(a>0)的焦点F的直线依次交抛物线及准线l于点A、B、C.若BC=2BF,AF=4,求a的值;
(4)【拓展升华】
古希腊数学家欧多克索斯在深入研究比例理论时,提出了分线段的“中末比”问题:点C将一条线段AB分为两段AC和CB,使得其中较长一段AC是全线段AB与另一段CB的比例中项,即满足:
=
=
.后人把
这个数称为“黄金分割”把点C称为线段AB的黄金分割点.
如图4所示,抛物线y=
x2的焦点F(0,1),准线l与y轴交于点H(0,﹣1),E为线段HF的黄金分割点,点M为y轴左侧的抛物线上一点.当
=
时,请直接写出△HME的面积值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd5daa9a0b9a14a4a44b02bae65b586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd5daa9a0b9a14a4a44b02bae65b586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd5daa9a0b9a14a4a44b02bae65b586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e28f005da664fc2f7ceacf1e32261e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
请分别直接写出抛物线y=2x2的焦点坐标和准线l的方程: , .
(2)【技能训练】
如图2所示,已知抛物线y=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
(3)【能力提升】
如图3所示,已知过抛物线y=ax2(a>0)的焦点F的直线依次交抛物线及准线l于点A、B、C.若BC=2BF,AF=4,求a的值;
(4)【拓展升华】
古希腊数学家欧多克索斯在深入研究比例理论时,提出了分线段的“中末比”问题:点C将一条线段AB分为两段AC和CB,使得其中较长一段AC是全线段AB与另一段CB的比例中项,即满足:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746853ea6d76bd7cccc6bdd6c739aed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e7e01495050cca64f635c2c2658157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d393bb07b7140905b85f550519de4.png)
如图4所示,抛物线y=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69d5b90c263274ccbdf1a0386e15110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
2022·湖北鄂州·中考真题 查看更多[9]
2022年湖北省鄂州市中考数学真题(已下线)专题22 与二次函数相关的压轴题-2022年中考数学真题分项汇编(全国通用)(第2期)(已下线)2022年湖北省随州市中考数学真题变式题21-24题(已下线)2022年湖北省鄂州市中考数学真题变式题21-24题(已下线)2022年湖北省武汉市中考数学真题变式题21-24题(已下线)二次函数的综合题03综合测(已下线)2023年新疆维吾尔族自治区中考数学真题变式题20-23题2024年广东省珠海市梅华中学中考一模数学试题2024年广东省惠州市惠阳区中考二模数学试题
更新时间:2022-06-28 09:21:21
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【推荐1】在平面直角坐标系
中,
,
,
在拋物线
上.
(1)抛物线的对称轴为直线
,直接写出
和
的大小关系
;
(2)若
,且
,则
的值是 .
(3)若对于任意
,都有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cc6b9d87d76c6392e8842bf9a9e9b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967c91dc7a77eb46e200c9ef6c32172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c75930c70cae009d373564d6b178d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/179d57d7f9be2f1c1a466fe4ee4d51e2.png)
(1)抛物线的对称轴为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1551f6bac6fea271cdbf902af2561fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5480081890562e2914de7e1386886ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4557a97a17857a08aeb0a39489f10b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】如图,抛物线
与x轴分别交于A,B两点(点A 在点B左侧).与y轴相交于点C,已知AB=4.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/24/d0f75463-1c1d-431d-b9f1-2458d50562e0.png?resizew=140)
(1)点A,B的坐标分别为______,______;
(2)c的值为______,抛物线的顶点坐标为______;
(3)设点P是y轴右侧抛物线上一动点,过点P作 PM//x轴交直线 BC于点M,当 PM≥2时,求点P的横坐标
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f09b500a60ed3a5d28eca9546b5de2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/24/d0f75463-1c1d-431d-b9f1-2458d50562e0.png?resizew=140)
(1)点A,B的坐标分别为______,______;
(2)c的值为______,抛物线的顶点坐标为______;
(3)设点P是y轴右侧抛物线上一动点,过点P作 PM//x轴交直线 BC于点M,当 PM≥2时,求点P的横坐标
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2297930d54a0452220d963bfef6a616a.png)
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解答题-作图题
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【推荐1】如图,四边形
为菱形,
于点,E是
上一点,且
,连接
.
(1)尺规作图:作
的外接圆
(保留作图痕迹);
(2)判断直线
与
的位置关系,并说明理由;
(3)连接
与
交于点
,若
,
,求菱形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa30a9ee227af2b387cf6e028c20d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d96a5d40d0aea9f4398ca4d0fe9b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/18/6dd2150d-921a-4e52-b458-d7acbe3f1c55.png?resizew=166)
(1)尺规作图:作
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441dec590b47adc3678a291a3ec89a4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(2)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
(3)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c3f982d999937891eec4cb22d62e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64e0206b1814c35cc96bd2b6b12239a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2a6932bdef68b0908011116bd08052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
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【推荐2】如图,
为
的直径,弦
于点
,且
为
的中点,
交
于点
,若
,动点
是
上一点,过点
作
的切线,交
的延长线于点
.
(1)求
的长;
(2)连接
,求证:
;
(3)当动点
在
的圆周上运动时,
的比值是否发生变化?若不变,求出比值;若变化,说明变化规律.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f986c181183d8e7e45655e6c5b5d5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af183f88ba4f7b9d370d49610cdf1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dea2ae9d515f9ab351ad72306b776ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/21/cecf1a1d-50c7-4dc7-b6e7-36c8ce0d726f.png?resizew=364)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e955767c01db5346211f4e2ec04d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17b89160163de99bfdc3f2676be5da9.png)
(3)当动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41ad2cd804093964a64a5736ba35dad.png)
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【推荐3】综合与实践课上,老师让同学们以“矩形与垂直”为主题开展数学活动.
如图1,正方形纸片
,在边
上任意取一点
,连接
,过点
作
于点
,与边
交于点
.
根据以上操作,请直接写出图1中
与
的数量关系:______.
(2)迁移探究
小华将正方形纸片换成矩形纸片,继续探究,过程如下:
如图2,在矩形纸片
中,
,在边
上任意取一点
,连接
,过点
作
于点
,与边
交于点
,请求出
的值,并说明理由;
(3)拓展应用
如图3,已知正方形纸片
的边长为
,动点
由点
向终点
做匀速运动,动点
由点
向终点
做匀速运动,动点
、
同时开始运动,且速度相同,连接
、
,交于点
,连接
,则线段
长度的最小值为______,点
的运动轨迹的长为______.(直接写出答案不必说明理由)
如图1,正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91cb9a5a14169845d700fbd95890ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
根据以上操作,请直接写出图1中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
(2)迁移探究
小华将正方形纸片换成矩形纸片,继续探究,过程如下:
如图2,在矩形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c691ca9b28ab952badcc89418d07e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb91cb9a5a14169845d700fbd95890ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c06aa28f4e4ee00cdf3c8e7847225ed.png)
(3)拓展应用
如图3,已知正方形纸片
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f887360a533f0a25b0b34fb11f0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8f887360a533f0a25b0b34fb11f0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
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【推荐1】元旦期间,嘉嘉和同学们一起到游乐场游玩,该游乐场大型摩天轮的示意图如图所示,摩天轮
的半径为
,摩天轮的圆周上均匀地安装了24个座舱(本题中将座舱视为圆周上的点),摩天轮匀速旋转一周需要30分钟,最底部离地面的高度
.嘉嘉和同学们分成3组在不同时间段进入座舱B,C,D,其中座舱C,D中间间隔3个座舱.
(1)连接
,则
的度数为________;当嘉嘉进入座舱C时,摩天轮旋转8分钟后,求座舱C走过的路程是多少?(结果保留π)
(2)在旋转一周的过程中,嘉嘉将有多长时间连续保持在离地面
及以上的空中?
(3)在水平地面
上有一动点P,连接
.在旋转过程中,若
与
相切,请直接 写出
长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40031deac58c539375624920eb1f534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/555ade0139feda7a60202e974279492e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/20/5cf17b3e-42a9-4d9b-9545-2f60f0bcb3de.png?resizew=139)
(1)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79179c5c6e4cae0ade3327d4fc6f9266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76bc8e50eeccced1d7f3bc52e09a7d03.png)
(2)在旋转一周的过程中,嘉嘉将有多长时间连续保持在离地面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccb003db7174ae33d5e6a9504671285.png)
(3)在水平地面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
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【推荐2】如图,以边长为
的正三角形纸板的各顶点为端点,在各边上分别截取
长的六条线段,过截得的六个端点作所在边的垂线,形成三个有两个直角的四边形.把它们沿图中虚线剪掉,用剩下的纸板折成一个底为正三角形的无盖柱形盒子,求它的容积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/58419997-bd57-4c00-8cf2-6e6c1ffe8034.png?resizew=224)
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【推荐1】如图,已知抛物线与
轴相交于点
,与
轴相交于
两点,点
的坐标为
,点
的坐标为
.
(1)求抛物线的函数表达式;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b00c9499415c5801c64a8177f4b35e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f510d788e893ee3410ae313658822bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0acc93490a6a784eb62201d93dd93d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)在直线
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147de24f071e316b68fd2e78e3c84545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐2】如图,抛物线y=ax2+bx+c交x轴于A(-1,0),B两点,交y轴于点C(0,3),顶点D的横坐标为1.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/28/ebe1b0be-f739-4955-a151-059ea52e5c8a.png?resizew=209)
(1)求抛物线的解析式;
(2)在y轴的负半轴上是否存在点P使∠APB+∠ACB=180°.若存在,求出点P的坐标,若不存在,请说明理由;
(3)过点C作直线l与y轴垂直,与抛物线的另一个交点为E,连接AD,AE,DE,在直线l下方的抛物线上是否存在一点M,过点M作MF⊥l,垂足为F,使以M,F,E三点为顶点的三角形与ΔADE相似?若存在,请求出M点的坐标,若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/28/ebe1b0be-f739-4955-a151-059ea52e5c8a.png?resizew=209)
(1)求抛物线的解析式;
(2)在y轴的负半轴上是否存在点P使∠APB+∠ACB=180°.若存在,求出点P的坐标,若不存在,请说明理由;
(3)过点C作直线l与y轴垂直,与抛物线的另一个交点为E,连接AD,AE,DE,在直线l下方的抛物线上是否存在一点M,过点M作MF⊥l,垂足为F,使以M,F,E三点为顶点的三角形与ΔADE相似?若存在,请求出M点的坐标,若不存在,请说明理由.
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