Problem 42840. Coefficients and vertex of a parabola given 3 points

Given 3 points, each defined by x and y, compute the coefficients: [a,b,c] of a parabola with equation: y = ax^2 + bx + c passing through those points. Also solve for the location of its vertex: [xv,yv].

Example:

 Inputs:  D = [0 3]; E = [1 6]; F = [-1 2]
 Outputs: C = [1 2 3]; V = [-1 2]
 Hence, the quadratic equation is: y = x^2 +2x + 3, with vertex at (-1,2)