Find the vertex of the parabola. y = - 4x2 - 16x - 11

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)