已知函數 y = (x-2)(2x-3) + x - k 的極貝值是 -8 , 求k的值

thank you

Note that
y = (x - 2)(2x - 3) + x - k
= 2x^2 - 7x + 6 + x - k
= 2(x^2 - 3x + 9/4) + 6 - k - 9/2
= 2(x - 3/2)^2 + 3/2 - k
Hence the minimum value = 3/2 - k = -8 ⇒ k = 3/2 + 8 = 19/2