We are asked to rewrite the quadratic equation 
in vertex form.
Vertex form is %7D%7D%5E%7B%7B2%7D%7D%2B%7Bk%7D "y=a(x-h)^2+k")
where the vertex is at (h,k). We will accomplish this by completing the square:
Now we add and subtract 36 (which is half of 12 squared)
The first three terms are a perfect square trinomial
%7D%7D%5E%7B%7B2%7D%7D-%7B39%7D "=(x-6)^2-39")
Thus the vertex form is %7D%7D%5E%7B%7B2%7D%7D-%7B39%7D "y=(x-6)^2-39")
with a vertex at (6,-39). The graph:
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