Đặt ` -4x^{2} + 8x + 24 = A `
Ta có:
` A = -4x^{2} + 8x + 24 `
` = -(4x^{2} - 8x - 24) `
` = -(2x - 2)^{2} + 28 `
Do: ` (2x - 2)^{2} ≥ 0 ` ` ∀ ` ` x ` ` ∈ ` ` R `
` => -(2x - 2)^{2} + 28 ≤ 28 `
` => A ≤ 28 `
Vậy ` A_max = 28, ` dấu ` "=" ` xảy ra khi: ` 2x - 2 = 0 <=> 2x = 2 <=> x = 1 `