Finding Coefficient b in a Quadratic Function

Let the function $f(x) = ax^2 + bx + c$ be defined in terms of its coefficients, where $a$, $b$, and $c$ are real numbers. It is known that the vertex of the parabola described by this function lies at the point $(4, -2)$. Additionally, when evaluated at $x = 0$, the function produces a value of $c = 5$. Given these conditions, determine the value of $b$ in the equation of the function. Please provide your answer as a decimal or fraction in the grid below.