Local quadratic approximation of a scale-space in image processing

Question

I'm dealing with a Local-approximation of a scale-space in image processing. The approximation I deal with reads as follows:
$L(u+\xi,v+\eta,\sigma)\approx L(u,v,\sigma)+\frac{\partial L}{\partial u} \cdot \xi+\frac{\partial L}{\partial v} \cdot \eta + \frac{1}{2}\cdot (\xi,\eta) \cdot \mathbf{H} \cdot (\xi,\eta)^T$
with $\mathbf{H}$ being the Hessian-Matrix. Now the next step in my text book is that they just leave out the middle part with the first partial derrivatives and say:
$=L(u,v,\sigma)+ \frac{1}{2}\cdot (\xi,\eta) \cdot \mathbf{H} \cdot (\xi,\eta)^T$
Why is that possible?