Advanced Quadratic Function Analysis

Consider a function defined by the quadratic equation:

$$f(x) = ax^2 + bx + c$$

Given that the vertex of the parabola opens upwards is at the point (2, -3), and that when $x = 0$, the output $f(0) = 1$. Moreover, it is known that $f(4) = 5$. Determine the values of coefficients $a$, $b$, and $c$. Using these coefficients, calculate the value of $f(1)$. Enter your answer as a decimal in the grid below.