Question

construa os graficos da função f(x)=x²+4x

Answer 1

$f(x)=x^2+4x\ \to\ a=1,\ b=4,\ c=0\\\\ \mathrm{V\acute{e}rtice}\ \to\ \boxed{V(x_V,y_V)=V\bigg(-\dfrac{b}{2a},-\dfrac{b^2-4ac}{4a}\bigg)}\ \therefore$

$x_V=-\dfrac{4}{2(1)}=-2,\ y_V=-\dfrac{4^2-4(1)(0)}{4(1)}=-4\ \therefore\ \boxed{V(-2,-4)}$

$\mathrm{Ra\acute{i}zes}\ \to\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-4\pm\sqrt{4^2-4(1)(0)}}{2(1)}=\\\\ =\dfrac{-4\pm4}{2}=-2\pm2\ \therefore\ \boxed{x_1=-4}\ \text{e}\ \boxed{x_2=0}$

$\text{Pontos}\ \to\ (-2,-4),\ (0,0),\ (-4,0)$

A partir desses três pontos, já é possível construir o gráfico.