Rewrite in vertex form by completing the square and stating the vertex y=x^2-12x-3

We are asked to rewrite the quadratic equation ` y=x^2-12x-3 ` in vertex form.

Vertex form is `y=a(x-h)^2+k ` where the vertex is at (h,k). We will accomplish this by completing the square:

`y=x^2-12x-3 ` Now we add and subtract 36 (which is half of 12 squared)

`=x^2-12x+36-36-3 ` The first three terms are a perfect square trinomial

`=(x-6)^2-39 `

Thus the vertex form is `y=(x-6)^2-39 ` with a vertex at (6,-39). The graph: