Quadratic interpolant for fixed f(x_0), f(x_1) and f'(x_0)

quadratic-interpolation.m

syms a b c x_0 x_1 f(x_0) f(x_1) df(x_0)
[a, b, c] = solve(...
      f(x_0) == a*x_0^2 + b*x_0 + c, ...
      f(x_1) == a*x_1^2 + b*x_1 + c, ...
      df(x_0) == 2*a*x_0 + b, ...
      a, b, c);
 
syms q(x)
q(x) = simplify(a*x^2 + b*x + c);