Question

Qual função do 2º grau representada no gráfico da figura abaixo? ​

Answer 1

$\boxed{\begin{array}{l}\sf O\,gr\acute afico\,passa\,pelos\,pontos\\\sf A(-1,0)~B(1,-4)~e~C(3,0)\\\sf f(x)=ax^2+bx+c\\\sf f(-1)=a\cdot(-1)^2+b\cdot(-1)+c\\\sf a-b+c=0\\\sf f(1)=a\cdot1^2+b\cdot1+c\\\sf a+b+c=-4\\\sf f(3)=a\cdot3^2+b\cdot3+c\\\sf 9a+3b+c=0\\\begin{cases}\sf a-b+c=0\\\sf a+b+c=-4\\\sf 9a+3b+c=0\end{cases}\\\\\begin{cases}\sf a+b+c=-4\\\sf a-b+c=0\\\sf 9a+3b+c=0\end{cases}\end{array}}$

$\boxed{\begin{array}{l}\begin{cases}\sf a+b+c=-4\\\sf -2b=4\\\sf-6b-8c=36\end{cases}\\\\\sf -2b=4\cdot(-1)\\\sf 2b=-4\\\sf b=-\dfrac{4}{2}\\\\\sf b=-2\\\sf -6b-8c=36\\\sf -6\cdot (-2)-8c=36\\\sf 12-8c=36\\\sf 8c=12-36\\\sf 8c=-24\\\\\sf c=-\dfrac{24}{8}\\\\\sf c=-3\\\sf a+b+c=-4\\\sf a-2-3=-4\\\sf a=2+3-4\\\sf a=1\end{array}}$

$\boxed{\begin{array}{l}\underline{\bf A\,func_{\!\!,}\tilde ao\,procurada\,\acute e}\\\huge\boxed{\boxed{\boxed{\boxed{\rm f(x)=x^2-2x-3}}}}\end{array}}$