Question

Find the parabola of the form y=ax^2+b which best fits the points (−1,0), (4,4), (5,8) by minimizing the sum, S, of squares of the vertical distances from the above points to the parabola given by: S=(a+b)^2+(16a+b−4)^2+(25a+b−8)^2. NOTE. You need to minimize S as a function of the variables a,b and then write the expression for y: y=ax^2+b with a and b that you have found.