如图,在平面直角坐标系中,抛物线y=ax²+bx+c的对称轴为直线x=-3/2,抛物线与x轴的交点为A、B,与y轴的交点为c,抛物线的顶点为M,直线MC的解析式是y=3\4x-2(1)求顶点M的坐标(2)求抛物线的解析式
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![如图,在平面直角坐标系中,抛物线y=ax²+bx+c的对称轴为直线x=-3/2,抛物线与x轴的交点为A、B,与y轴的交点为c,抛物线的顶点为M,直线MC的解析式是y=3\4x-2(1)求顶点M的坐标(2)求抛物线的解析式](/uploads/image/z/2089338-42-8.jpg?t=%E5%A6%82%E5%9B%BE%2C%E5%9C%A8%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BB%E4%B8%AD%2C%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dax%26sup2%3B%2Bbx%2Bc%E7%9A%84%E5%AF%B9%E7%A7%B0%E8%BD%B4%E4%B8%BA%E7%9B%B4%E7%BA%BFx%3D-3%2F2%2C%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8Ex%E8%BD%B4%E7%9A%84%E4%BA%A4%E7%82%B9%E4%B8%BAA%E3%80%81B%2C%E4%B8%8Ey%E8%BD%B4%E7%9A%84%E4%BA%A4%E7%82%B9%E4%B8%BAc%2C%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E9%A1%B6%E7%82%B9%E4%B8%BAM%2C%E7%9B%B4%E7%BA%BFMC%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%E6%98%AFy%3D3%5C4x-2%281%29%E6%B1%82%E9%A1%B6%E7%82%B9M%E7%9A%84%E5%9D%90%E6%A0%87%EF%BC%882%EF%BC%89%E6%B1%82%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F)
如图,在平面直角坐标系中,抛物线y=ax²+bx+c的对称轴为直线x=-3/2,抛物线与x轴的交点为A、B,与y轴的交点为c,抛物线的顶点为M,直线MC的解析式是y=3\4x-2(1)求顶点M的坐标(2)求抛物线的解析式
如图,在平面直角坐标系中,抛物线y=ax²+bx+c的对称轴为直线x=-3/2,抛物线与x轴的交点为A、B,
与y轴的交点为c,抛物线的顶点为M,直线MC的解析式是y=3\4x-2
(1)求顶点M的坐标(2)求抛物线的解析式(3)以线段AB为直径做圆P,判断直线MC与圆P的位置关系,并证明你的结论
如图,在平面直角坐标系中,抛物线y=ax²+bx+c的对称轴为直线x=-3/2,抛物线与x轴的交点为A、B,与y轴的交点为c,抛物线的顶点为M,直线MC的解析式是y=3\4x-2(1)求顶点M的坐标(2)求抛物线的解析式
(1)顶点在对称轴 x= -3/2上
MC的解析式是y= (3/4)x - 2
x = -3/2,y = -9/8 -2 = -25/8
M(-3/2,-25/8)
(2) y = ax²+bx+c = a[x + b/(2a)]²+ c -b^2/(4a)
对称轴为x = -b/(2a) = -3/2,b= 3a (a)
C(0,-2)
-2 = 0 + 0 +c
c = -2 (b)
顶点M纵坐标 c -b^2/(4a) = -25/8 (c)
(a)(b)(c):a = 1/2,b = 3/2
求抛物线的解析式:y = (1/2)x² + (3/2)x - 2
(3) y = (1/2)x² + (3/2)x - 2 = 0
(x+4)(x-1)= 0
A(-4,0),B(1,0)
半径 = (1+4)/2 = 5/2
圆心P(-3/2,0)
直线MC的解析式是y= (3/4)x - 2,3x - 4y - 8 = 0
圆心和直线MC的距离:|3(-3/2) - 4*0 -8|/√(3²+4²) = (25/2)/5 = 5/2,等于半径,直线MC与圆相切