Question

Complete the square to rewrite y = x^2 + 6x + 3 in vertex form. Then state whether the vertex is a maximum or a minimum and give its coordinates.

Answer 1

Let's complete the square first.

y = x² + 6x + 3

= (x² + 6x + 9) - 6

= (x + 3)² - 6

Therefore, the vertex is (-3, -6) and since the coefficient of (x + 3)² is positive, the vertex is a minimum.