Question

Considere uma fun¸c˜ao polinomial do segundo grau definida por f(x) = x 2 − 4x + 3. O gr´afico que representa essa fun¸c˜ao ´e uma par´abola, que possui v´ertice V (a, b). O valor de (a + b) ´e igual a:

Answer 1

$\boxed{\mathbf{f(x)=x^2-4x+3}}\ \to\ \mathrm{a=1;\ b=-4;\ c=3}\\\\ \mathrm{V\acute{e}rtice\ \to\ \boxed{\mathrm{V(x_v;y_v)=V(a,b)}}}$

$\mathbf{Encontrando\ o\ valor\ de\ a\ (x_v):}\\\\ \mathrm{\boxed{\mathrm{x_v=-\dfrac{b}{2a}}}\ \to\ x_v=-\dfrac{-4}{2.1}=\dfrac{4}{2}=2\ \to\ \boxed{\mathbf{a=2}}}$

$\mathbf{Encontrando\ o\ valor\ de\ b\ (y_v):}\\\\ \mathrm{\boxed{\mathrm{y_v=-\dfrac{\Delta}{4a}=-\dfrac{b^2-4ac}{4a}}}\ \to\ y_v=-\dfrac{(-4)^2-4.1.3}{4.1}=}\\\\\\ \mathrm{=-\dfrac{16-12}{4}=-\dfrac{4}{4}=-1\ \to\ \boxed{\mathbf{b=-1}}}$

$\mathbf{Problema\ final:}\\\\ \mathrm{V\acute{e}rtice\ \to\ \boxed{\mathrm{V(a;b)=V(2;-1)}}}\\\\ \mathrm{a+b=2+(-1)=2-1=1}\\\\ \mathrm{Resposta\ \to\ \boxed{\boxed{\mathbf{1}}}}$