f(x,y) = a*x**2 + b*y**2 + c*x*y + d*x + e*y + g
f(0,0) = 0
f(1,1) = 1
df/dx(0,0) = 0
df/dy(0,0) = 0
df/dx(1,1) = 0
df/dy(1,1) = 0