Calculate quadratic function from given points in 2 dimensions

Question

The quadratic function can be defined as
$z = a+b*x+c*y+d*x^2 +e*x*y+f*y^2$
But how to find the 6 coefficients from given truples $(x_i,y_i,z_i)$?
I hope that there is a not too difficult solution. Can anybody give me a reference? In opposite to e.g. solving a cubic equation in 1D I found nothing unfortunately.