Does the path the football follows after being kicked represent a linear or nonlinear function? explain.

No it is parabolic in shape because it rises and then falls because of gravity.  We normally, for simplicity's sake assume gravity is constant and also ignore air resistance, but it is MOSTLY parabolic in shape.  When we do so we model it with a quadratic equation because quadratics have a constant acceleration or if you prefer d2y/dx2=k.