Assume that A=(x1,y1) B=(x2,y2) C=(x3,y3) are points with distinct x-coordinates. To illustrate that the points lie on the parabola y=ax^2+bx+c do the following
i) substitute given points in to equation of the parabola and set up the linear system in variables a, b and c.
ii) Illustrate that determinant of coefficient matrix is (x2-x1) (x3-x1) (x3-x2).
iii) Use determinant from (b) to describe why linear system has the unique solution.
iv) Determine equation of polynomial passing through A=(1,-1) B=(2,4) and C=(3,3) by first verifying there exists the unique solution.