(a) Using R, generate a fake data set of 50 points along a parabola (i.e. a quadratic polynomial) with two real roots. Whether or not you add noise is up to you.

(b) Estimate the parameters ri in y = (x r1)(x r2) or (x r1)(x r2) based on graphically inspecting the data (e.g. plot it and carefully read off where the roots occur).

(c) Fit the function y = a+b x+c x2 to your simulated data using two different methods in optimx() (e.g., use method=c("Nelder-Mead","BFGS")). Use the quadratic formula to calculate the roots ri , and compare to part (b).