What is the value of h when the function is converted to vertex form? note: vertex form is g(x)=a(x-h)^2 +k g(x)=x^2-6x+14 h=?

There are two ways you can solve this problem.
The first is to solve g(x) into vertex and see what number is in H's spot.
The second is to ind the vertex point and the opposite sign of X is H.
I will do both.

First way:
Subtract 14 from both sides
Y-14=X^2-6X
Add to the right side whatever will make it a perfect square. (This will be -6 divided by 2 then squared: -6/2=-3, (-3)^2=9)
Add 9 to BOTH sides.
y-5=X^2-6X+9
Factor the right side
y-5+=(x-3)^2
Add 5 to both sides
y=((X-3)^2)+5

3 is in H's spot.

Second way:
Find the axis of symmetry (b/(2a)) 
-6/(2*1)=-3
-3 is the X-value of the vertex. In vertex form, H is the opposite sign of the X-Value. So the opposite sign of -3 is positive 3.