Consider a trebuchet launching a flaming stone over a castle wall. It is mounted on a small hill and has a parabolic trajectory (neglecting air resistance). Once it crashes into the ground on the other side of the castle wall, it comes to rest. This motion is described by the function below, where x, measured in meters, represents horizontal displacement from the launch position and y = f(x) represents vertical distance from the ground, measured in meters.
f(x) = -0.25x2 + 3.15x + 5
Determine the contextual domain and range and justify your answers. What is the peak height of the flaming stone?