Question

Para quais valores reais de x a função

Answer 1

$\Large\boxed{\begin{array}{l}\sf y=-x^2+x+6\\\sf\Delta=b^2-4ac\\\sf\Delta=1^2-4\cdot(-1)\cdot6\\\sf\Delta=1+25\\\sf\Delta=25\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-1\pm\sqrt{25}}{2\cdot(-1)}\\\\\sf x=\dfrac{-1\pm5}{-2}\begin{cases}\sf x_1=\dfrac{-1+5}{-2}=\dfrac{4}{-2}=-2\\\\\sf x_2=\dfrac{-1-5}{-2}=\dfrac{-6}{-2}=3\end{cases}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm a)~\sf se\,anula\,para\,x=-2~ou~x=3\\\rm b)~\sf se\,torna\,positiva\,para\,-2 < x < 3\\\rm c)~\sf se\,torna\,negativa\,para\,x < -2~ou~x > 3\end{array}}$