Linear algebra help me understand

Please explain completely and show work. I want to understand what this means. We all know from Euclidean geometry that two points define a unique linear function. By simple antidifferentiation principles, one needs three noncollinear points to define a unique quadratic function, and by induction, one needs n + 1 noncollinear points to define a unique n"th degree polynomial function. Suppose that you are given (1, 2), (-1, 6), and (2, 3). Using matrix methods for solving systems of equations, find the unique quadratic function that passes through these given points. No fair using your calculator's regression capabilities or matrix capabilities. Now suppose that you are given (1, 0), (-1, -24), (2, 0), and (4, 6). Using matrix methods for solving systems, find the unique cubic function that passes through these given points. No fair using your calculator's regression capabilities or matrix capabilities