注:x^2的系数大于0,二次函数像开口向上,没有最大值,只有最小值.这里假定二次函数为
y = -x^2 + mx + n
(1) y = -x^2 + mx _+n = -(x - m/2)^2 + n + m^2/4
x= m/2时有最大值n + m^2/4:3= m/2,m = 6; n + m^2/4 = 4
n = 4 - (-6)^2/4 = -5
(2) y = -x^2 + 6x -5 = -(x -5)(x - 1)
与x轴的交点:A(5,0),B(1,0)
(3) 圆经过A B且与y轴的正半轴相切,圆心必然在AB的中垂线(x = 3)上且半径为中垂线的横坐标3.设方程3为(x -a)^2 + (y - b)^2 = 9
代入A(5,0),B(1,0)
(a - 5)^2 + b^2 = 9
(a -1)^2 + b^2 = 9
(a-5)^2 = (a-1)^2
a -5 = a -1 (无解)
或 a -5 = 1-a,a =3
b=±√5 (负值舍去,因与y轴的正半轴相切)
(x -3)^2 + (y - √5)^2 = 9
C的纵坐标与圆心纵坐标相同
C(0,√5)