Question 771638
The actual variables will be D, E, and F.  The x and y values will become constants or part of constants.  The system of equations will be more comfortable with each equation in the form, {{{xD+yE+F=-x^2-y^2}}}.


Each point gives one equation:
SYSTEM:
{{{1D+1E+F=-1-1}}}
{{{2D-1E+F=-2^2-(-1)^2}}}
{{{2D+3E+F=-2^2-3^2}}}
'
SIMPLIFIED SYSTEM:
---------------------------
{{{D+E+F=-2}}}
{{{2D-E+F=-5}}}
{{{2D+3E+F=-13}}}
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You can solve for the three variables any way you know or like.  You can also solve using the matrix,

 
{{{(
matrix(3,4,
1,1,1,-2,
2,-1,1,-5,
2,3,1,-13)
)}}}


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Intentionally unfinished allowing you to finish yourself.