Write the function $LaTeX: \displaystyle f(x)=x^{2} + 12 x + 71$ 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 $LaTeX: \displaystyle k = 35$ . The vertex is located at $LaTeX: \displaystyle (-6,35)$ and the vertex form is $LaTeX: \displaystyle f(x) = a(x-h)^2+k=\left(x + 6\right)^{2} + 35$ .