Suppose that you are given three points (x0, f(x0)), (x1, f(x1)), (x2, f(x2)). (a) Find the equation of the parabola y = ax2 + bx + c that passes through those 3 points. (b) Find the point x3 where the parabola intersects the x axis. (c) Give an algorithm based on your previous answers that can be used to approximate a solution to the equation f(x) = 0 given three initial guesses x0, x1, x2.

This is for a class on Numerical Methods, some of the things we've covered are Bisection, Newton's Algorithm, Horner's Method, etc.

Thanks!