$\sum_i\left(y_i-y_0-a(x_i^2-x_0^2)-b(x_i-x_0)\right)^2=min$

sum_i(y_i-y_0-a(x_i^2-x_0^2)-b(x_i-x_0))^2=min

$a=\displaystyle\frac{((NS_{x2}-S_x^2)x_0^2+(S_xS_{x2}-NS_{x3})x_0+S_xS_{x3}-S_{x2}^2)y_0+(S_xS_y-NS_{xy})x_0^3+(-2S_{x2}S_y+S_xS_{xy}+NS_{x2y})x_0^2+(S_{x3}S_y+S_{x2}S_{xy}-2S_xS_{x2y})x_0-S_{x3}S_{xy}+S_{x2}S_{x2y}}{(NS_{x2}-S_x^2)x_0^4+(2S_xS_{x2}-2NS_{x3})x_0^3+(NS_{x4}+2S_xS_{x3}-3S_{x2}^2)x_0^2+(2S_{x2}S_{x3}-2S_xS_{x4})x_0+S_{x2}S_{x4}-S_{x3}^2}$

a=(((NS_x2-S_x^2)x_0^2+(S_xS_x2-NS_x3)x_0+S_xS_x3-S_x2^2)y_0+(S_xS_y-NS_xy)x_0^3+(-2S_x2S_y+S_xS_xy+NS_x2y)x_0^2+(S_x3S_y+S_x2S_xy-2S_xS_x2y)x_0-S_x3S_xy+S_x2S_x2y)/((NS_x2-S_x^2)x_0^4+(2S_xS_x2-2NS_x3)x_0^3+(NS_x4+2S_xS_x3-3S_x2^2)x_0^2+(2S_x2S_{x3}-2S_xS_x4)x_0+S_x2S_x4-S_x3^2)

$b=-\displaystyle\frac{((NS_{x3}-S_xS_{x2})x_0^2+(S_{x2}^2-NS_{x4})x_0+S_xS_{x4}-S_{x2}S_{x3})y_0+(S_xS_y-NS_{xy})x_0^4+(NS_{x2y}-S_{x2}S_y)x_0^3+(-S_{x3}S_y+2S_{x2}S_{xy}-S_xS_{x2y})x_0^2+(S_{x4}S_y-S_{x2}S_{x2y})x_0-S_{x4}S_{xy}+S_{x2y}S_{x3}}{(NS_{x2}-S_x^2)x_0^4+(2S_xS_{x2}-2NS_{x3})x_0^3+(NS_{x4}+2S_xS_{x3}-3S_x2^2)x_0^2+(2S_{x2}S_{x3}-2S_xS_{x4})x_0+S_{x2}S_{x4}-S_{x3}^2}$

b=-(((NS_x3-S_xS_x2)x_0^2+(S_x2^2-NS_x4)x_0+S_xS_x4-S_x2S_x3)y_0+(S_xS_y-NS_xy)x_0^4+(NS_x2y-S_x2S_y)x_0^3+(-S_x3S_y+2S_x2S_xy-S_xS_x2y)x_0^2+(S_x4S_y-S_x2S_x2y)x_0-S_x4S_xy+S_x2yS_x3)/((NS_x2-S_x^2)x_0^4+(2S_xS_x2-2NS_x3)x_0^3+(NS_x4+2S_xS_x3-3S_x2^2)x_0^2+(2S_x2S_x3-2S_xS_x4)x_0+S_x2S_x4-S_x3^2)

$a=\displaystyle\frac{S_{x2}S_{x2y}-S_{x3}S_{xy}}{S_{x2}S_{x4}-S_{x3}^2}$

a=(S_x2S_x2y-S_x3S_xy)/(S_x2S_x4-S_x3^2)

$b=\displaystyle\frac{S_{x4}S_{xy}-S_{x2y}S_{x3}}{S_{x2}S_{x4}-S_{x3}^2}$

b=(S_x4S_xy-S_x2yS_x3)/(S_x2S_x4-S_x3^2)

$ S_{xnym} =\displaystyle\sum_i^N x_i ^n y_i ^m$

S_xnym = @SUM( x_i ^n* y_i ^m, i , 1 , N )