  In this paper, we give quadratic approximation of generalized Tribonacci
sequence $\{V_{n}\}_{n\geq0}$ defined by Eq. (\ref{eq:7}) and use this result
to give the matrix form of the $n$-th power of a companion matrix of
$\{V_{n}\}_{n\geq0}$. Then we re-prove the cubic identity or Cassini-type
formula for $\{V_{n}\}_{n\geq0}$ and the Binet's formula of the generalized
Tribonacci quaternions.
