Given the table:

(a,b) |  f  |  f_x |  f_y | f_xx | f_yy | f_yx
----------------------------------------------
(1,2) |  5  |   2  |  -4  |  12  |  10  |  -8

Find Q(x,y) the quadratic polynomial for f(x,y) 
near (1, 2).


Answer (note it is equal, not approximately equal)
Q(x,y) = 5 + 2(x-1) -4(y-2)+ [12(x-1)^2 + (2)(-8)(x-1)(y-2) + 10(y-2)^2]/2!