Question

2. 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 + Ipoints to define a unique nh 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.

please explain step by step

Answer 1