We have the function:

$\displaystyle f(x,y)=32xy^2-20xy^3-3x^3y+4$

Find the approximating quadratic polynomial with the development points: $\displaystyle (x_0,y_0)=(0,1)$

I've found it to be:

$\displaystyle z=4+8x+4xy$

Now find the type, vertex and line of symmetry for the graph the approximating quadratic polynomial produces.

I had to translate it to English, but hopefully it is understandable and if not I'll try to explain the question differently.