Can you solve for a b and c in the quadratic equation with only a list of data points?
Yes. You need at least three points with x and y coordinates for
this.
Let the points be: A(x1, y1), B(x2, y2) and C(x3, y3).
For each of the points yi = ax2i + bxi + c,
so you have to solve a set of simultaneous equations for i=1 ...
3(the y's and x's are no longer variables! the a, b, c are!):
y1 = ax21 + bx1 + c,
y2 = ax22 + bx2 + c,
y3 = ax23 + bx3 + c