Question

抛物线Y=X2+4mx+m-3的顶点坐标在直线y=x-4上，m=?

Answer 1

首先配方，变成顶点坐标式 y = a(x - h)" + k
y = x" + 4mx + m - 3
= x" + 2(2m)x + (2m)" - 4m" + m - 3
= (x + 2m)" + ( -4m" + m - 3)

抛物线的顶点坐标（h ，k ），就是（-2m ，-4m" +m -3）
顶点坐标在直线 y = x - 4 上面，
那么 k = h - 4
-4m" + m - 3 = -2m - 4
-4m" + 3m + 1 = 0
解方程
4m" - 3m - 1 = 0
4m" - 4m + m - 1 = 0
4m (m - 1) + (m - 1) = 0
(m - 1)(4m + 1) = 0
m1 = 1
m2 = -1/4