Écrire chaque fonction polynôme du second degré sous forme canonique. En déduire le tableau de variations correspondant à chaque fonction. a.x²-8x +9 b.-2x² + 6

forme canonique : ax² + bx + c = a(x-alpha)²+beta

alpha = -b/2a

beta = -(b-4ac)²/2a

a)

a = 1

b = -8

c = 9

alpha = 8/2×1 = 8/2 = 4

beta = -(-8-4×1×9)²/2×1 = (8+4×9)²/2 = (8+36)²/2 = 44²/2 = 1936 = 968

forme canonique : 1(x-4)²+968

b)

a = -2

b = 6

c = 1

alpha = -6/2×(-2) = -6/-4 = 1,5

beta = -(6-4×(-2)×1)²/2×(-2) = -(6-(-8))²/-4 = -(6+8)²/-4 = 196/-4 = -49

forme canonique : -2(x-1,5)²-49

c)

a = 16

b = 0

c = -1

alpha = 0/2×16 = impossible

forme canonique impossible