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