; Combine 3 quadratic polynomials with 3 unknown coefficients (a, b, c).
; Solve for a, b, and c.

clear all
y1=a+b*x1+c*x1^2
y2=a+b*x2+c*x2^2
y3=a+b*x3+c*x3^2
2 ; select equation number 2
eliminate a ; eliminate variable (a) from the current equation
3 ; select equation number 3
eliminate a b ; eliminate variables (a) and (b)
c ; solve for c
2 ; select equation number 2 again
eliminate c using 3 ; eliminate (c) using equation number 3
1 ; select equation number 1
eliminate b c ; the final elimination
simplify all ; list all solutions
fraction all ; convert to simple fractions