5. A quantity y is known to depend on another quantity x. A set of corresponding values has been collected for x and y as presented in the following table. Fit the best quadratic curve y = ax² + bx+c to the data points with an objective function
(a) such that the sum of absolute deviation of all corresponding values are minimized.
(b) such that the maximum deviation is minimized.
x 0.0 0.5 1.0 1.5 1.9 2.5 3.0 3.5 4.0 4.5 5.0 6.0 6.6
y 1.0 0.9 0.7 1.5 2.0 2.4 3.2 2.0 2.7 3.5 1.0 4.0 3.6