Answer:
h=4
Step-by-step explanation:
The given function is
[tex]h(x)=x^2-8x+14[/tex]
We add and subtract the square of half the coefficient of x.
[tex]h(x)=x^2-8x+(\frac{-8}{2})^2-(\frac{-8}{2})^2+14[/tex]
[tex]h(x)=x^2-8x+(-4)^2-(-4)^2+14[/tex]
The first three terms forms a perfect square trinomial
[tex]h(x)=(x-4)^2-16+14[/tex]
[tex]h(x)=(x-4)^2-2[/tex]
We now compare to the vertex form;
[tex]h(x)=a(x-h)^2+k[/tex]
We have h=4
