Answer:
The given equation for the path of the football is f(x) = -2(x-3)^2 + 56.
This is a quadratic function in the form f(x) = a(x-h)^2 + k, where a, h, and k are constants.
Comparing this equation to the standard form, we can see that a = -2, h = 3, and k = 56.
Since the coefficient of the squared term is negative, the graph of this quadratic function is a downward-facing parabola.
The maximum height reached by the football occurs at the vertex of the parabola.
The x-coordinate of the vertex is given by x = h = 3.
The y-coordinate of the vertex is given by f(h) = k = 56.
Therefore, the maximum height reached by the football is 56 feet.
Explanation: