Question

A função f(x) = - x ^ 2 + 6x + k tem o valor máximo igual a 25. Qual é o valor de k?​

Answer 1

$\boxed{\begin{array}{l}\sf f(x)=-x^2+6x+k\\\sf\Delta=b^2-4ac\\\sf\Delta=6^2-4\cdot(-1)\cdot k\\\sf\Delta=36+4k\\\sf y_V=-\dfrac{\Delta}{4a}\\\\\sf 25=-\dfrac{36+4k}{4\cdot(-1)}\\\\\sf 25=\dfrac{36+4k}{4}\\\\\sf 4k+36=100\\\sf 4k=100-36\\\sf 4k=64\\\sf k=\dfrac{64}{4}\\\\\sf k=16\end{array}}$