The standard equation is y=ax^2+bx+k and the vertex way is y=a(x-h)(x-h)+x
so the coordinate for x is -b/2a, for your problem a=-4 b=-16 so the coordinate for x is -(-16)/(2*(-4))=-2. Now you have to replace x=-2 in your equation y=-4(-2)^2-16(-2)-11= 5.
The vertex is (-2, 5)
