Write the function $LaTeX: \displaystyle f(x)=x^{2} - 12 x + 12$ in vertex form and identify the vertex.

$LaTeX: \displaystyle h = -\frac{b}{2a}$ and $LaTeX: \displaystyle k=f(h)$ . Using each formula gives $LaTeX: \displaystyle h= 6$ and $LaTeX: \displaystyle k = -24$ . The vertex is located at $LaTeX: \displaystyle (6,-24)$ and the vertex form is $LaTeX: \displaystyle f(x) = a(x-h)^2+k=\left(x - 6\right)^{2} - 24$ .