Réponses

Meilleure réponse !
2014-09-07T11:36:35+02:00
1)
f(x) = 4x² - 4x + 4
la forme canonique est de la forme f(x) = a(x-\alpha)^2+\beta

a = 4\\
\alpha =  \frac{-(-4)}{2\times4}= \frac{1}{2}\\\\
\beta=f(\alpha)=4\times( \frac{1}{2})^2-4\times \frac{1}{2}+4=  3\\\\
\boxed{f(x) =4(x- \frac{1}{2} )^2+3}

2)
f(x) = 4(x-2)^2-16\\
f(x) = 4(x-2)^2-4^2\\
f(x) = 4(x-2-4)(x-2+4)\\\boxed{f(x) = 4(x-6)(x+2)}

3)
f(x) = 2(3-2x)(x+2)\\
f(x) = 6x+12-4x^2-8x\\
f(x) = -4x^2-2x+12

la forme canonique est de la forme f(x) = a(x-\alpha)^2+\beta

a = -4\\
\alpha=  \frac{-(-2)}{2\times(-4)}= \frac{1}{4}\\\\
\beta=f(\alpha) = -4\times( \frac{1}{4})^2-2\times \frac{1}{4}+12 =  \frac{45}{4}\\\\
\boxed{f(x) = -4(x- \frac{1}{4})^2+ \frac{45}{4}  }