duanyifan
幼苗
共回答了15个问题采纳率:93.3% 举报
已知抛物线
![](https://img.yulucn.com/upload/e/2b/e2b39270a8b71c8829f4d536bbefd9b2_thumb.jpg)
(其中a ≠ c且a ≠0).
(1)求此抛物线与x轴的交点坐标;(用a,c的代数式表示)
(2)若经过此抛物线顶点A的直线
![](https://img.yulucn.com/upload/1/75/175a616d30937d30b8ada187bebcd4a7_thumb.jpg)
与此抛物线的另一个交点为
![](https://img.yulucn.com/upload/c/03/c0311053d728c51dfa2f8e3f3cbbcf69_thumb.jpg)
,
求此抛物线的解析式;
(3)点P在(2)中x轴上方的抛物线上,直线
![](https://img.yulucn.com/upload/1/75/175a616d30937d30b8ada187bebcd4a7_thumb.jpg)
与 y轴的交点为C,若
![](https://img.yulucn.com/upload/9/5c/95cf1ba12a65b441eef98563f04c611d_thumb.jpg)
,求点P的坐标;
(4)若(2)中的二次函数的自变量x在n≤x<
![](https://img.yulucn.com/upload/3/84/3845efcc50799d6cef6cb0905e5a8b05_thumb.jpg)
(n为正整数)的范围内取值时,记它的整数函数值的个数为N, 则N关于n的函数关系式为 .
(1)
![](https://img.yulucn.com/upload/1/dc/1dc99a0f5ed544f81d1b17364407a125_thumb.jpg)
,
(2)
(3)
(4)
(1)抛物线
![](https://img.yulucn.com/upload/e/2b/e2b39270a8b71c8829f4d536bbefd9b2_thumb.jpg)
与x轴交点的横坐标是关于x的方程
![](https://img.yulucn.com/upload/3/7c/37c6b161b0c9c6db57b727476114ea46_thumb.jpg)
(其中a ≠ 0,a ≠c)的解.
解得
![](https://img.yulucn.com/upload/7/dd/7ddb8b51e60c4d0461c38df4a3076871_thumb.jpg)
,
![](https://img.yulucn.com/upload/2/0d/20daa05ccb6d6d3f58870fce4fc036cc_thumb.jpg)
. ………………………………………………………… 1分
∴ 抛物线与x轴交点的坐标为
![](https://img.yulucn.com/upload/1/dc/1dc99a0f5ed544f81d1b17364407a125_thumb.jpg)
,
![](https://img.yulucn.com/upload/9/5f/95fc3af1f26fae7ec31678f2e936d853_thumb.jpg)
.……………………………… 2分
(2)抛物线
![](https://img.yulucn.com/upload/e/2b/e2b39270a8b71c8829f4d536bbefd9b2_thumb.jpg)
的顶点A的坐标为
![](https://img.yulucn.com/upload/d/7f/d7f4063d8ed9fb2ca5cb4de864808392_thumb.jpg)
.
∵ 经过此抛物线顶点A的直线
![](https://img.yulucn.com/upload/1/75/175a616d30937d30b8ada187bebcd4a7_thumb.jpg)
与此抛物线的另一个交点为
![](https://img.yulucn.com/upload/c/03/c0311053d728c51dfa2f8e3f3cbbcf69_thumb.jpg)
,
由③得 c ="0. " ……………………………………………………………3分
将其代入①、② 得
解得
![](https://img.yulucn.com/upload/d/ba/dba9e0e0d8ba6ecc4374852b2e0a057d_thumb.jpg)
.
∴ 所求抛物线的解析式为
![](https://img.yulucn.com/upload/5/44/54495ea142b79cd78f5f9d21f9c97205_thumb.jpg)
.…………………………………… 4分
(3)作PE⊥x轴于点E, PF⊥y轴于点F.(如图7)
抛物线
![](https://img.yulucn.com/upload/5/44/54495ea142b79cd78f5f9d21f9c97205_thumb.jpg)
的顶点A的坐标
![](https://img.yulucn.com/upload/6/59/6590cd2902e22b63887895519a11967c_thumb.jpg)
,
点B的坐标为
![](https://img.yulucn.com/upload/1/dc/1dc99a0f5ed544f81d1b17364407a125_thumb.jpg)
,点C的坐标为
![](https://img.yulucn.com/upload/c/c3/cc357dd449c076ee627d36d20f37d1ec_thumb.jpg)
.
设点P的坐标为
![](https://img.yulucn.com/upload/1/0d/10d4c48be71e97a47f5708a9b136fbd9_thumb.jpg)
.
∵ 点P在x轴上方的抛物线
![](https://img.yulucn.com/upload/5/44/54495ea142b79cd78f5f9d21f9c97205_thumb.jpg)
上,
∴
![](https://img.yulucn.com/upload/0/d2/0d2d0f8e638075a2d92acffcc435f864_thumb.jpg)
,且0<m<1,
![](https://img.yulucn.com/upload/7/24/72493446b99f53dee74df59765cff02f_thumb.jpg)
.
∴
![](https://img.yulucn.com/upload/b/a0/ba0dce500d7c3756763b9c449003d3d0_thumb.jpg)
,
![](https://img.yulucn.com/upload/e/70/e707cf6273355939a2f912c7723537af_thumb.jpg)
.
∵
![](https://img.yulucn.com/upload/9/5c/95cf1ba12a65b441eef98563f04c611d_thumb.jpg)
,
∴
![](https://img.yulucn.com/upload/a/e1/ae193e65dd66aaceb8b7ff0f14e3d82f_thumb.jpg)
.
解得 m=2n,或
![](https://img.yulucn.com/upload/e/fb/efbaca2d2d479f64b3eb559d93aab629_thumb.jpg)
(舍去). ………………………………………………5分
将m=2n代入
![](https://img.yulucn.com/upload/0/d2/0d2d0f8e638075a2d92acffcc435f864_thumb.jpg)
,得
![](https://img.yulucn.com/upload/7/86/7860c2f6e0d8ddf227e9c5222a6b2b35_thumb.jpg)
.
解得
![](https://img.yulucn.com/upload/1/9d/19deefd8e02cb3f1d5b513d6e0eaee25_thumb.jpg)
,
![](https://img.yulucn.com/upload/b/2f/b2f62c9f23a18307bf2cb87e070214bf_thumb.jpg)
(舍去).
∴
![](https://img.yulucn.com/upload/c/c2/cc25fa11acc8d6ed841357f9bf6681e7_thumb.jpg)
.
∴ 点P的坐标为
![](https://img.yulucn.com/upload/3/39/3397b9ce1e67b88f4b55f82c3842816a_thumb.jpg)
. …………………………………………………………6分
(4)N关于n的函数关系式为N="4n" . ………………………………………………7分
说明:二次函数
![](https://img.yulucn.com/upload/5/44/54495ea142b79cd78f5f9d21f9c97205_thumb.jpg)
的自变量x在n≤x<
1年前
10