Solve 3 quadratics simultaneously given (x,y)

I am trying to solve a system of quadratic equations.

Given:

y1 = a*x1^2 + b*x1 + c

y2 = a*x2^2 + b*x2 + c

y3 = a*x3^2 + b*x3 + c

(x1, y1), (x2, y2), (x3, y3)

I need to solve for a,b,c.

Trying to use Gaussian Elimination does not seem to give any success.

Does anyone have any idea where to find a solution to this? I have checked out the web on solving for the three-point quadratic, but nothing shows the algorithm.

Solving 3 Quadratics simultaneously

After reading the various replies to this query, I do not think I stated my intentions clearly. I am trying to solve for a parabola that passes through three points.

Given 3 points (x1, y1), (x2, y2), (x3, y3), where x1=x, x2=x+1, x3=x+2

I want to solve the three equations simultaneously to get one generic equation for those three points. So obviously the three equations to solve simultaneously for would be

y1 = a*x1^2 + b*x1 + c = a*x^2 + bx + c

y2 = a*x2^2 + b*x2 + c = a*(x+1)^2 + bx + b + c = ax^2 + 2ax + a + bx + b + c

y3 = a*x3^2 + b*x3 + c = a*(x+2)^2 + bx + 2b + c = ax^2 + 4ax + 4a + bx + 2b + c

Sorry for any confusion caused.