Réponse :
Explications étape par étape
Bonjour
Relier forme développée et forme canonique
Forme développée :
• -3x^2 - 6x - 7 = -3(x + 1)^2 - 4
• -3x^2 + 6x - 1 = -3(x - 1)^2 + 2
• 3x^2 + 24x + 53 = 3(x + 4)^2 + 5
• 3x^2 - 12x + 15 = 3(x - 2)^2 + 3
• 3x^2 - 12x + 5 = 3(x + 2)^2 - 7
• 3x^2 - 24x + 1 ? Il y a une erreur c’est + 49 sinon la dernière expression ne correspond pas
• 3(x + 4)^2 + 5 = 3(x^2 + 8x + 16) + 5 = 3x^2 + 24x + 48 + 5 = 3x^2 + 24x + 53
• -3(x - 1)^2 + 2 = -3(x^2 - 2x + 1) + 2 = -3x^2 + 6x - 3 + 2 = -3x^2 + 6x - 1
• -3(x + 1)^2 - 4 = -3(x^2 + 2x + 1) - 4 = -3x^2 - 6x - 3 - 4 = -3x^2 - 6x - 7
• 3(x + 2)^2 - 7 = 3(x^2 + 4x + 4) - 7 = 3x^2 + 12x + 12 - 7 = 3x^2 + 12x + 5
• 3(x - 4)^2 + 1 = 3(x^2 - 8x + 16) + 1 = 3x^2 - 24x + 48 + 1 = 3x^2 - 24x + 49
• 3(x - 2)^2 + 3 = 3(x^2 - 4x + 4) + 3 = 3x^2 - 12x + 12 + 3 = 3x^2 - 12x + 15
Relier forme factorisee et forme canonique :
Forme factorisee :
• 3(x - 1)(x + 2) = 3(x + 1/2)^2 - 27/4
• 3(x + 2)(x - 3) = 3(x - 1/2)^2 - 75/4
• 3(x + 1)(x + 2) = 3(x + 3/2)^2 - 3/4
• 3(x - 1)(x - 2) = 3(x - 3/2)^2 - 3/4
• 3(x + 3)(x + 2) = 3(x + 5/2)^2 - 3/4
Forme canonique :
• 3(x + 3/2)^2 - 3/4 = 3[(x + 3/2)^2 - (1/2)^2] = 3(x + 3/2 - 1/2)(x + 3/2 + 1/2) = 3(x + 2/2)(x + 4/2) = 3(x + 1)(x + 2)
• 3(x + 5/2)^2 - 3/4 = 3[(x + 5/2)^2 - (1/2)^2] = 3(x + 5/2 - 1/2)(x + 5/2 + 1/2) = 3(x + 2)(x + 3)
• 3(x - 1/2)^2 - 75/4 = 3[(x - 1/2)^2 - (5/2)^2] = 3(x - 1/2 - 5/2)(x - 1/2 + 5/2) = 3(x - 3)(x + 2)
• 3(x + 1/2)^2 - 27/4 = 3[(x + 1/2)^2 - (3/2)^2] = 3(x + 1/2 - 3/2)(x + 1/2 + 3/2) = 3(x - 1)(x + 2)
• 3(x - 3/2)^2 - 3/4 = 3[(x - 3/2)^2 - (1/2)^2] = 3(x - 3/2 - 1/2)(x - 3/2 + 1/2) = 3(x - 2)(x - 1)
