Question

Sendo f(x)=-3x²+4x-4, para qual valor de x tem-se f(x)=-8 ? *

Answer 1

$f(x)=-3x^2+4x-4$

$f(x)=-8$

$-3x^2+4x-4=-8$

$-3x^2+4x-4+8=0$

$-3x^2+4x+4=0$

$\triangle=b^2-4.a.c=4^2-4.(-3).4=16+48=64$

$x_1=\frac{-b+\sqrt{\triangle} }{2a}= \frac{-4+\sqrt{64} }{2.(-3)}=\frac{-4+8}{-6}=\frac{4}{-6}=-\frac{2}{3}$

$x_2=\frac{-b-\sqrt{\triangle} }{2a}= \frac{-4-\sqrt{64} }{2.(-3)}=\frac{-4-8}{-6}=\frac{-12}{-6}=2$

$f(x)=-8$ quando "x" assume os valores $-\frac{2}{3}$ ou $2$