What are the coordinates of the vertex of y = –x2 – 12x – 32?

The answer to your question is     Vertex = (-6 , 4)

Step-by-step explanation:

Data

Equation    y = -x² - 12x - 32

Process

1.- Add 32 units in both sides

                 y + 32 = -x² - 12x - 32 + 32

2.- Simplify

                 y + 32 = -x² - 12x

3.- Factor -1 in the right side

                 y + 32 = -(x² + 12x       )

4.- Complete the perfect square trinomial

                 y + 32 - 6²  = -(x² + 12x + 6²)

5.- Simplify

                 y + 32 - 36 = -(x + 6)²

                           y - 4 = -(x + 6)²

6.- Find the vertex

                          Vertex = (-6 , 4)