Hi Andrik,
I'm not sure why you are calling these equations 'inequalities', but if you are looking for a numerical solution to this, then you can use the backslash solution method that Matlab was basically founded on.
xCoords = [4 2 7]';
yCoords = [1 3 -4]';
syms a b c
eq1 = a*xCoords(1)^2+b*xCoords(1)+c; % equation 1
eq2=a*xCoords(2)^2+b*xCoords(2)+c;% equation 2
eq3=a*xCoords(3)^2+b*xCoords(3)+c; % equation 3
final_eq = solve([eq1==yCoords(1), eq2==yCoords(2), eq3 == yCoords(3)]);
var_a = abs(final_eq.a)
var_b = (final_eq.b)
var_c = (final_eq.c)
% numerical linalg solution
% form the vandermonde matrix (xCoords and yCoords are column vectors)
vander = [xCoords.^2 xCoords ones(size(xCoords))]
abc = vander\yCoords % abc(1) = var_a, etc.
The linalg solution gives the same result except in double precision rather than the fractions produced by sym. Also the sign of var_a is different because the linalg solution has not yet taken the absolute value of that variable.
