如图,已知二次函数y=ax2-2ax+3(a<0)的图象与x轴的负半轴交于点A,与y轴的正半轴交于点B,顶点为P,且OB=3OA,一次函数y=kx+b的图象经过点A、点B(1)求一次函数的解析式;(2)求顶点P的坐标;(
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/26 04:37:33
![如图,已知二次函数y=ax2-2ax+3(a<0)的图象与x轴的负半轴交于点A,与y轴的正半轴交于点B,顶点为P,且OB=3OA,一次函数y=kx+b的图象经过点A、点B(1)求一次函数的解析式;(2)求顶点P的坐标;(](/uploads/image/z/4328136-0-6.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%B7%B2%E7%9F%A5%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0y%3Dax2-2ax%2B3%EF%BC%88a%EF%BC%9C0%EF%BC%89%E7%9A%84%E5%9B%BE%E8%B1%A1%E4%B8%8Ex%E8%BD%B4%E7%9A%84%E8%B4%9F%E5%8D%8A%E8%BD%B4%E4%BA%A4%E4%BA%8E%E7%82%B9A%2C%E4%B8%8Ey%E8%BD%B4%E7%9A%84%E6%AD%A3%E5%8D%8A%E8%BD%B4%E4%BA%A4%E4%BA%8E%E7%82%B9B%2C%E9%A1%B6%E7%82%B9%E4%B8%BAP%2C%E4%B8%94OB%3D3OA%2C%E4%B8%80%E6%AC%A1%E5%87%BD%E6%95%B0y%3Dkx%2Bb%E7%9A%84%E5%9B%BE%E8%B1%A1%E7%BB%8F%E8%BF%87%E7%82%B9A%E3%80%81%E7%82%B9B%EF%BC%881%EF%BC%89%E6%B1%82%E4%B8%80%E6%AC%A1%E5%87%BD%E6%95%B0%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%E9%A1%B6%E7%82%B9P%E7%9A%84%E5%9D%90%E6%A0%87%EF%BC%9B%EF%BC%88)
如图,已知二次函数y=ax2-2ax+3(a<0)的图象与x轴的负半轴交于点A,与y轴的正半轴交于点B,顶点为P,且OB=3OA,一次函数y=kx+b的图象经过点A、点B(1)求一次函数的解析式;(2)求顶点P的坐标;(
如图,已知二次函数y=ax2-2ax+3(a<0)的图象与x轴的负半轴交于点A,与y轴的正半轴交于点B,顶点为P,且OB=3OA,一次函数y=kx+b的图象经过点A、点B
(1)求一次函数的解析式;
(2)求顶点P的坐标;
(3)平移直线AB使其过点P,如果点M在平移后的直线上,且tan∠OAM=2/3
,求点M的坐标
我只要第三问,
如图,已知二次函数y=ax2-2ax+3(a<0)的图象与x轴的负半轴交于点A,与y轴的正半轴交于点B,顶点为P,且OB=3OA,一次函数y=kx+b的图象经过点A、点B(1)求一次函数的解析式;(2)求顶点P的坐标;(
(1)
x = 0, y = 3, B(0, 3)
设A(-p, 0), 则OB = 3 = 3p, p = 1
A(-1, 0)
x = -1, y = a + 2a + 3 = 3a + 3 = 0, a = -1
一次函数的解析式: x/(-1) + y/3 = 1, y = 3(x + 1)
(2)
y = -x² + 2x + 3 = -(x - 1)² + 4
P(1, 4)
(3)
y = 3(x + 1) = 3x + 3
平移后变为 y = 3x + b
过点P: 4 = 3*1 + b, b = 1
y = 3x + 1
M(m, 3m + 1)
tan∠OAM = M的纵坐标/AO = (3m + 1)/[m - (-1)] = (3m + 1)/(m + 1) = 2/3
m = -1/7
M(-1/7, 4/7)