What are the coordinates of the vertex for f (x) = x2 + 4x + 10?

F (x) = x² + 4x + 10

f (x) - 10 = x² + 4x

perfect square:

x² + 4x + 4 ⇒ (x + 2) ²

(x + 2) ² = x (x+2) + 2 (x+2) = x² + 2x + 2x + 4 = x² + 4x + 4

f (x) - 10 + 4 = x² + 4x + 4

f (x) - 6 = (x+2) ²

f (x) = (x+2) ² + 6