Hi,



 a = 8, length of the transverse axis(distance between the vertices) = 16

Note: Standard Form of an Equation of an Hyperbola opening right and  left is:

   with C(h,k) and vertices 'a' units right and left of center,   2a the length of the transverse axis

Foci are  units right and left of center along y = k

& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 



G(x) = (x - 8)^2 + 6 has the same shape as F(x) = x^2 + 6, how far to the right of F(x) is G(x) shifted? 

G(x) = (x - 8)^2 + 6  parabola V(8,6)

F(x) = x^2 + 6 parabola V(0,6)

G(x) shifted 8 units to the right 

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