Answer
$f(x)=(x-4)^2-15$
Work Step by Step
Completing the square:
$f(x)=x^2-8x+1$
$f(x)=x^2-8x+(\frac{8}{2})^2-(\frac{8}{2})^2+1$
$f(x)=x^2-8x+4^2-4^2+1$
$f(x)=(x-4)^2-16+1$
$f(x)=(x-4)^2-15$
Graphing the function:
1st step (black graph): The parent function: $y=x^2$
2nd step (green graph): Shift down by 15 units. $y=x^2-15$
Final step (blue graph): Shift right by 4 units. $y=(x-4)^2-15$
