What is the vertex of the graph of this equation y= -4x^2-16x-12

One way to locate the vertex is to obtain the coefficients a, b and c from the quadratic and then calculate  
                                      -(-16)
x = -b / (2a).  Here, x = = -2
                                       2(-4)

Next, evaluate y at x = -2:  y = -4(-2)^2 - 16(-2) - 12 = -16 + 32  - 12
                                           y = 4

the vertex is at (-2,4).