Question 194512
Let  H(x) = y
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y = (x-6)^2  +1
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(y-1) = (x-6)^2,,,,,from  this  we  can  read,  vertex  at  (6,1),  
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positive  leading  coefficient  means  it  is  pointing  up
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Axis  of  symmetry  is   x=6
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another  form  might  be,,, y=x^2 -12x +36 +1  =  x^2 -12x +37
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vertex  of  x  is  -b/2a  =  -(-12)/2(1) =  +6,,, subst in  to  get  y= 1,,,,( 6,1)
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check  by  plotting  a  few  points,  (6,1),,,,(5,2),,,,(7,2)