✨ 最佳解答 ✨
y = ax^2 +bx +c 有最大值 = -6
= a(x^2 + b/a x) +c
= a(x + b/2a)^2 +c - b^2/4a
當 x = -b/2a 時，有最大值或最小值 c - b^2/4a
a:b:c = 1:2:3
假設 a = x, b = 2x, c = 3x
3x - 4x^2/4x = -6 (4x不能約掉，不然就少掉一個解了)
12x^2 -4x^2 = -24x
8x^2 +24x = 0
x^2 +3x = 0
x(x+3) = 0
x = 0 or -3
=> y = -3x^2 -6x -9
y = -3x^2 +2x -k
= -3(x^2 -2/3x) +k
= -3 (x - 1/3)^2 -k +1/3
當 x = 1/3 時 有最大值 1/3 -k
另外一個 y = k-1
1/3 -k = k-1 (剛好相交時)
2k = 4/3
k = 2/3
好哦謝謝