Question

What is the value of h when the function is converted to vertex form?

Answer 1

Completing the squqre:

h(x) = x^2 - 8x + 14  =  x^2 - 8x + 16 - 16 + 14  =  (x-4)^2 - 2

Here h=4 and k = -2.

Answer 2

$f(x)=ax^2+bx+c\\\\h=\dfrac{-b}{2a};\ k=f(h)$

We have:
$h(x)=x^2-8x+14\\\\a=1;\ b=-8;\ c=14$

Substitute:
$h=\dfrac{-(-8)}{2\cdot1}=\dfrac{8}{2}=4$