Answered

Bonjour,
on me donne ces 3 expressions : [tex]f(x)=(x+ \frac{1}{3}) ^{2} - 4(x- \frac{1}{3}) ^{2} [/tex]
f(x) =[tex]-3 x^{2} + \frac{10}{3}x- \frac{1}{3} [/tex]
f(x) =[tex](3x- \frac{1}{3})(-x+1) [/tex]

Et je dois démontrer que f(x)= [tex]-3((x- \frac{5}{9}) ^{2} - \frac{16}{81}) [/tex]
Merci de votre aide. :)

Sagot :

forme factorisée
f(x)=(x+1/3)²-4(x-1/3)²
=(x+1/3)²-(2x-2/3)²
=(x+1/3+2x-2/3)(x+1/3-2x+2/3)
=(3x-1/3)(-x+1)

forme développée
f(x)=(x+1/3)²-4(x-1/3)²
=x²+2x/3+1/9-4x²+8x/3-4/9
=-3x²+10x/3-1/3

forme canonique
f(x)=(x+1/3)²-4(x-1/3)²
=-3x²+10x/3-1/3
=-3(x²-10x/9)-1/3
=-3((x-5/9)²-25/81)-1/3
=-3(x-5/9)²+25/27-1/3
=-3(x-5/9)²+16/27
=-3((x-5/9)²-16/81)