Question

uma função quadrática f é tal que f(0)=-2, f(1)=2 e f(-1)=-4. obtenha f(2) e assinale a alternativa correta.
alguem me ajuda na Minha prova​

Answer 1

$\large\boxed{\begin{array}{l}\rm f(0)=-2~~f(1)=2~~f(-1)=-4\\\rm f(0)=a\cdot 0^2+b\cdot 0+c\longrightarrow c=-2\\\rm f(1)=a\cdot 1^2+b\cdot 1-2\\\rm a+b-2=2\\\rm a+b-2=2\\\rm a+b=2+2\longrightarrow a+b=4\\\rm f(-1)=a\cdot(-1)^2+b\cdot(-1)-2\\\rm a-b-2=-4\\\rm a-b=2-4\\\rm a-b=-2\end{array}}$

$\large\boxed{\begin{array}{l}\sf montando\,um\,sistema\,temos:\\+\underline{\begin{cases}\rm a+\backslash\!\!\!b=4\\\rm a-\backslash\!\!\!b=-2\end{cases}}\\\rm 2a=2\\\rm a=\dfrac{2}{2}\longrightarrow a=1\\\rm a+b=4\\\rm 1+b=4\\\rm b=4-1\\\rm b=3\\\\\rm f(x)=x^2+3x-2\\\rm f(2)=2^2+3\cdot2-2\\\rm f(2)=4+6-2\\\rm f(2)=8\\\green{\huge\boxed{\boxed{\boxed{\boxed{\rm\dagger\red{\maltese}~\blue{alternativa~b}}}}}}\end{array}}$