x^2-4x-17 is the same as 1x^2 + (-4)x + (-17)
It is in the form y = ax^2 + bx + c where
a = 1
b = -4
c = -17
To find the value of h, we use this formula
h = -b/(2a)
h = -(-4)/(2*(1))
h = 4/2
h = 2
Plug this back into the original function to find k
k = x^2-4x-17
k = (2)^2-4(2)-17
k = 4-8-17
k = -4-17
k = -21
So we know that a = 1, h = 2 and k = -21 making
y = a(x-h)^2 + k
turn into
y = 1(x-2)^2 - 21
which is now in vertex form. The vertex is (h,k) = (2,-21)