The general expression for Taylor series is given here.
My book says we can write the Taylor series about origin $(0,0)$ as:
$f(x,y)=\dfrac{1}{2} [f_{xx}\ x^2 + 2f_{xy}\ xy + f_{yy}\ y^2]$
because the linear terms vanish because of the position of the axes.
Is this perfectly correct about $(0,0)$ or is it an approximation?