Question

已知二次函数Y=AX+BX+C的图象以X=1为对称轴,且过点《-1,0》和《0,3》求此函数图象

Answer 1

已知对称轴,可设：y = m(x - 1)^2 + n

将《-1,0》和《0,3》代入得方程组：

0 = m(-1 - 1)^2 + n

3 = m(0 - 1)^2 + n

即

4m + n = 0

m + n = 3

则

m = -1

n = 4

所以,y = -(x - 1)^2 + 4 = -x^2 + 2x +3