명제와 조건

Following is a statement of a theorem which can be proven using calculus or precalculus mathematics. For this theorem, $a$, $b$, and $c$ are real numbers.

• Theorem If $f$ is a quadratic function of the form $f\left( x \right) = ax^2 + bx + c$ and $a \lt 0$, then the function $f$ has a maximum value when $x = \dfrac{{ - b}}{{2a}}$.

Using only this theorem, what can be concluded about the functions given by the following formulas?

$k\left( x \right) = 8x^2 - 5x - 7$