Linear interpolation formula $$ g(x)=f_j+\frac{x-x_j}{x_{j+1}-x_j}(f_{j+1}-f_i) $$ where answer is $ y=ax+b $ can be changed to $$ a=\frac{f_{j+1}-f_j}{x_{j+1}-x_j} \\b=f_j-x_j\frac{f_{j+1}-f_j}{x_{j+1}-x_j} $$ so it can be programmed in C language, where you can't calculate with few unknown variables.
Can someone help me transform/find already transformed second degree polynomial interpolation formula $$ g(x) = f_j \frac{(x-x_{j+1})(x-x_{j+2})}{(x_j-x_{j+1})(x_j-x_{j+2})}+ \\+f_{j+1} \frac{(x-x_j)(x-x_{j+2})}{(x_{j+1}-x_j)(x_{j+1}-x_{j+2})}+ \\f_{j+2} \frac{(x-x_j)(x-x_{j+1})}{(x_{j+2}-x_j)(x_{j+2}-x_{j+1})} $$ where answer is $ y=ax^2+bx+c $ like in linear interpolation example where it would be solvable for $a, b$ and $c$ having data table and not knowing $ x $ .