How Do You Put A Quadratic Equation In Vertex Form?

The desired form is
  (y - k) = a(x - h)²
where (h, k) is the vertex.
We start with the general form of the quadratic.
  Y = ax² + bx + c
  (y - c)/a = x² + (b/a)x    (subtract c from both sides, divide both sides by a. We do this to make it easier to see the "completing the square" operation we will be doing on the right side of the equation.)
  (y - c)/a + b²/(4a²) = x² + (b/a)x + b²/(4a²)    (add a term to both sides that makes the right side a perfect square. That term is (b/(2a))²)
  (y - c + b²/(4a))/a = (x + b/(2a))²     (show the right side as a perfect square. Add the terms on the left side and express over a common denominator.)
  (y - (c - b²/(4a))) = a(x - (-b/(2a)))²    (this is the desired form)
Note that (h, k) = (-b/(2a), c - b²/(4a))