Question

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

Answer 1

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