Answer :
Genaral equation of a parabola: y = ax^2 + bx + c
X of the vertex: x = -b/2a
In this case a = -1, b = 8 and c = -19
Therefore X for the vertex is x = -8/(2)(-1) = -8/-2 = 4
To find the Y of the vertex, we use the original equation an the value we just foud for X
y = -x^2 + 8x - 19
y = -(4)^2 + 8(4) - 19
y = -16 + 32 - 19
y = -3
So the vertex is (4, -3)