二次函数解析
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/09/03 04:20:55
解题思路: 利用二次函数的性质求解。
解题过程:
![](http://img.wesiedu.com/upload/5/12/512cef6128bb8e5f9d332d5eecac08a3.png)
解:(1)过点
![](http://img.wesiedu.com/upload/b/b0/bb01cb2c880538ddf5c6f3679e73574e.png)
作
![](http://img.wesiedu.com/upload/1/79/179c7436ca1174ef64ece0687a104132.png)
轴,垂足为点
![](http://img.wesiedu.com/upload/e/48/e48d25ebbbea6c7e52588ac6eb956e3b.png)
,过点
![](http://img.wesiedu.com/upload/2/78/2781d15ea33b7debe6dadc32788b4bf6.png)
作
![](http://img.wesiedu.com/upload/4/12/4121f194f47c16c9e49c4b67404090ba.png)
轴,垂足为点
![](http://img.wesiedu.com/upload/d/eb/deb095905af3802443b48ea18d2128b8.png)
, 则
![](http://img.wesiedu.com/upload/2/ba/2bac37600d9d3e58b4e15efebc0e5f1c.png)
.
![](http://img.wesiedu.com/upload/d/55/d55d8ea05ac32983c68a41e3563fec6e.png)
,
![](http://img.wesiedu.com/upload/d/69/d6965eb9c31b435cbedca726ca766347.png)
. 又
![](http://img.wesiedu.com/upload/4/3f/43f227cb92c05c3905ea5eac0cb57260.png)
,
![](http://img.wesiedu.com/upload/a/ee/aeeea77d1fe4fc4cd7426e90fbee6e0c.png)
.
![](http://img.wesiedu.com/upload/b/ff/bffa9343a39d3bbb4dcde712c6961213.png)
.
![](http://img.wesiedu.com/upload/0/d1/0d1a0340a42e909137431705cb777bd5.png)
.
![](http://img.wesiedu.com/upload/d/61/d61c073b93e7ef83167b72c480a76c67.png)
.
![](http://img.wesiedu.com/upload/d/dc/ddc939deff5df38e92dd093bd3ba55e6.png)
. (2)设过点
![](http://img.wesiedu.com/upload/9/a4/9a47b90c2c9dcd51aea65aad6f031e18.png)
,
![](http://img.wesiedu.com/upload/e/95/e9553f98e1cfc4acf53c3cf85dd24114.png)
,
![](http://img.wesiedu.com/upload/b/72/b72521e6a5a867c3028bbcb91622bcc7.png)
的抛物线为
![](http://img.wesiedu.com/upload/c/ff/cff332a22938d3ac5b8f4770397ce1a6.png)
.
![](http://img.wesiedu.com/upload/0/cc/0cc67d3c4a02a453e986a59b48d82d27.png)
解之,得
![](http://img.wesiedu.com/upload/2/13/21343b1ed2f3da2a0030ad289aec37d8.png)
所求抛物线的表达式为
![](http://img.wesiedu.com/upload/a/2a/a2a69dcf40aa1fd1a852741893a3d816.png)
. (3)由题意,知
![](http://img.wesiedu.com/upload/2/31/23135cf348e2b9f6014fee6438c534e9.png)
轴. 设抛物线上符合条件的点
![](http://img.wesiedu.com/upload/6/1a/61a5988ae0906af61025ac969f7086a2.png)
到
![](http://img.wesiedu.com/upload/b/98/b9837b5e5db18cf268238e0c90005158.png)
的距离为
![](http://img.wesiedu.com/upload/b/e3/be344ef94c72b44a63e8e96c5b1ada00.png)
,则
![](http://img.wesiedu.com/upload/e/43/e4324ea5c26fd0459c84462f16801d1b.png)
.
![](http://img.wesiedu.com/upload/8/d1/8d1b8d4b5aeedf7b8f37203559ede10b.png)
.
![](http://img.wesiedu.com/upload/2/13/21343b1ed2f3da2a0030ad289aec37d8.png)
点
![](http://img.wesiedu.com/upload/6/1a/61a5988ae0906af61025ac969f7086a2.png)
的纵坐标只能是0,或4. 令
![](http://img.wesiedu.com/upload/c/cb/ccbd5981b03f153998b0e9051948ff4e.png)
,得
![](http://img.wesiedu.com/upload/9/09/909511bae5848377feae12cc7571b348.png)
.解之,得
![](http://img.wesiedu.com/upload/b/bc/bbcdd88dbed19019967f92ef610ab4e7.png)
,或
![](http://img.wesiedu.com/upload/9/40/940e51bd2d7eb9e4573c0a502bc7bb3d.png)
.
![](http://img.wesiedu.com/upload/2/13/21343b1ed2f3da2a0030ad289aec37d8.png)
符合条件的点
![](http://img.wesiedu.com/upload/e/4f/e4fbd707d9efa8f47cd52e947db59277.png)
,
![](http://img.wesiedu.com/upload/1/3c/13c8f574f0127ad457cc4d5f9806ec75.png)
. 令
![](http://img.wesiedu.com/upload/9/9b/99b983445e6ac77d23edb40aa234df3e.png)
,得
![](http://img.wesiedu.com/upload/7/15/7151f36959d3580a729f3708ca57eb68.png)
.解之,得
![](http://img.wesiedu.com/upload/6/98/698ff4d9086f2d00760a65ae682c2fda.png)
.
![](http://img.wesiedu.com/upload/2/13/21343b1ed2f3da2a0030ad289aec37d8.png)
符合条件的点
![](http://img.wesiedu.com/upload/3/ca/3cad911e8b5304fb08a6163eed9f18c0.png)
,
![](http://img.wesiedu.com/upload/4/9f/49f35cbec22872769cc4d7e3fe367b7d.png)
.
![](http://img.wesiedu.com/upload/2/13/21343b1ed2f3da2a0030ad289aec37d8.png)
综上,符合题意的点有四个:
![](http://img.wesiedu.com/upload/e/4f/e4fbd707d9efa8f47cd52e947db59277.png)
,
![](http://img.wesiedu.com/upload/1/3c/13c8f574f0127ad457cc4d5f9806ec75.png)
,
![](http://img.wesiedu.com/upload/3/ca/3cad911e8b5304fb08a6163eed9f18c0.png)
,
![](http://img.wesiedu.com/upload/4/9f/49f35cbec22872769cc4d7e3fe367b7d.png)
.
最终答案:略