Question

represente graficamente : equação do 2 grau

y=x²-4x

Answer 1

$\text{Vamos l\'a:}\\\\\\y=x^2-4x~~\text{(iguale a fun\c{c}\~ao a 0 e aplique Bhaskara)}\\\\\\x^2-4x=0\\\\\\\fbox{\fbox{ \dfrac{-b\pm\sqrt{\Delta}}{2a} }}\\\\\\\Delta=b^2-4\cdot a\cdot c\\\\\\\Delta=(-4)^2-4\cdot 1\cdot 0\\\\\\\Delta=16-0\\\\\\\Delta=16$



$\dfrac{-(-4)\pm\sqrt{16}}{2\cdot 1}\\\\\\=\dfrac{4\pm4}{2}~^\Rightarrow~\dfrac{4+4}{2}~\Rightarrow~\dfrac{8}{2}=4~~\text{(Solu\c{c}\~ao 1, raiz 1)}\\\\\\ \dfrac{4-4}{2}~\Rightarrow~ \dfrac{0}{2}=0~~\text{(Solu\c{c}\~ao 2, raiz 2)}\\\\\\\text{Portanto a par\'abola ir\'a tocar o eixo x em x = 4 e x = 0}$



$\text{Obs: como o coeficiente a \'e positivo, a par\'abola apresenta concavidade}\\\text{para cima.}$