Consider the Four Points a = (1, 0), B = $y = a x ^ { 2 } + b x + c$

Essay

Consider the four points A = (1, 0), B = (2, 3), C = (3, 5)and D = (4, 3)in the xy-plane.
Find the values of a, b and c to determine the parabola of best fit, $y = a x ^ { 2 } + b x + c$ for these points.
(The parabola of best fit minimizes the sum of the squares of the vertical distances from each point to the parabola.)