This quadratic function is in vertex form, which is

#y = a(x - h)^2 + k#, where #(h, k)# is the vertex of the graph of the function. Also, if #a >0#, the parabola will open upward and the #y#-coordinate of the vertex will be the minimum value of the curve. If #a <0#, the parabola will open downward and the #y#-coordinate of the vertex will be the maximum value of the curve.

In #y = -2(x + 5)^2 - 8#, #a = -2# and #-2 < 0#, so the parabola will open downward and the maximum value of the curve will be the #y#-coordinate of the vertex, or #k#. In this equation, #k = -8#, so the maximum valu of the function is #-8#.