Find symmetric matrix of polynomial equation Let f be a polynomial such that $x, y, z, t$ belong to $\mathbb{R}^4$.
$$f(x) = 4x^2+4y^2+4z^2+4t^2+8xy+6xt+6yz+8zt$$
Find the symmetric matrix and determine whether $A$ is a positive definite or not.
I understand how to find a symmetric matrix and check whether or not it is a positive matrix. I'm having trouble starting. Would I change this equation to a matrix?
Any guidance on how to start this problem would be appreciated. 

$\begin{eqnarray*}f(x) &=& 4x^2+4y^2+4z^2+4t^2+8xy+6xt+6yz+8zt\\
&=&\begin{bmatrix} x&y&z&t \end{bmatrix}
\begin{bmatrix} 4&4&0&3\\4&4&3&0\\0&3&4&4\\3&0&4&4 \end{bmatrix}
\begin{bmatrix}x\\y\\z\\t\end{bmatrix}
\end{eqnarray*}
$

 It's eigenvalues are -3, 3, 5, 11,so it's not positive definite.
