In order to find the vertex, consider that the x-coordinate of the vertex is given by:
x = -b/2a
where b and a are the coefficient of the polynomial ax² + bx + c. By comparing it with the given polynomial you have:
a = -1
b = 6
x = -6/(2(-1))
x = 3
next, to find the y coordinate of the vertex, evaluate the x coordinate into f(x):
f(3) = -(3)² + 6(3) - 1
f(3) = 8
Hence, the vertex of the given function is:
(3 , 8)