25Completing the square

Write $\displaystyle y = x^2 - 6x + 11$ in vertex form and give the vertex.

The vertex form is y = (x − 3)² + 2, so the vertex is (3, 2). Completing the square: half of −6 is −3, squared is 9, giving (x−3)² + 11 − 9 = (x−3)² + 2. Check: at x=3, 9−18+11 = 2, matching the vertex.