Write this function in vertex form, and Identify its vertex x^2-4x-17

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)