[Lagrange Multipliers]

Given the 5 points, (-2,4), (-1,2), (0,1), (1,1), and (2,2):

a) Find the equation that best fits this data (in the sense of
least squares).

b) Find the best fitting quadratic (parabola) for these five
points (in the sense of least square). [Hint: Use the same method
as was used in finding the best fit line, only with a quadratic
function of the form p(x)=ax^2+bx+c. Find a, b, and c that
minimizes the sum of the square errors between the actual data and
the values on the parabola.]