The axis of symmetry for the function  f(x) =  −x2 − 10x + 16 is x = −5. what are the coordinates of the vertex of the graph?

Do this by completing the square.  Start by setting the function equal to 0 and at the same time moving the constant over to the other side of the equals sign. .  The rules for completing the square is the leading coefficient has to be a positive 1, but ours is -1, so we have to factor out the negative, and when we do that, we have this: .  10x is our linear term.  We will take half of tha 10 to get 5, square the 5 to get 25 and add 25 to both sides.  HOWEVER, that -1 is still hanging around out front, so what we actually have "added" in is -1(25) = -25.  So now what we have is this: .  In this process we have created a perfect square binomial on the left: .  Now we will move the -41 by adding to get .  Our vertex, then, is (-5, 41).