Answer
$f(x)=(x-4)^2-15$
See graph
Work Step by Step
We are given the function:
$f(x)=x^2-8x+1$
Complete the square:
$f(x)=x^2-8x+16-16+1=(x-4)^2-15$
We start graphing with the basic function $a(x)=x^2$.
We horizontally shift $a(x)$ by 4 units to the right to get $b(x)=(x-4)^2$.
Then we vertically shift $b(x)$ 15 units downwards to get $f(x)=(x-4)^2-15$.
We use 3 points: $(0,1),(4,-16),(8,1)$