Complete the square to rewrite y = x ^ 2 + 6x + 5 in vertex form. Then state whether the vertex is a maximum or a minimum and give its coordinates.

y = (x + 3) ² - 4

The vertex is a minimum at (-3, - 4)

Step-by-step explanation:

Step 1: Isolate xs

y - 5 = x² + 6x

Step 2: Complete the square

y - 5 + 9 = x² + 6x + 9

y + 4 = (x + 3) ²

Step 3: Convert to vertex form

y = (x + 3) ² - 4

To find your vertex, (h, k) is your vertex, so (-3, - 4). To see whether or not it is a max or a min, check a to see if it is positive or negative. Since a is positive, it is a minimum.