Question

2. Aflați coordonatele vârfului parabolei asociate funcției f:R → R, f(x) = x² - 4x +2.
3. Rezolvaţi în mulțimea numerelor reale ecuația log3x = log3(4-x).​

Answer 1

 

$\displaystyle\bf\\2)\\f:R\to R,~~f(x)=x^2-4x+2\\\\Cazul~generalL~~f(x)=ax^2+bx+c\\a=1\\b=-4\\c=2\\\\Se~cer:\\\textbf{Coordonatele varfului parabolei asociate functiei.}\\\\V(x_v;~y_v)\\\\x_v=\frac{-b}{2a}=\frac{-(-4)}{2\times1}=\frac{4}{2}=\boxed{\bf2}\\\\y_v=\frac{-\Delta}{4a}=\frac{-(b^2-4ac)}{4a}=\frac{-(16-4\times2)}{4}=\frac{-8}{4}=\boxed{\bf-2}\\\\ V(x_v;~y_v)=\boxed{\bf V(2;~-2)}\\\\\\3)\\log_3(x)=log_3(4-x)\\\\x=4-x\\\\2x=4\\\\x=\frac{4}{2}\\\\\boxed{\bf x=2}$