Answer
$f(x)=(x-3)^2-9$
See graph
Work Step by Step
We are given the function:
$f(x)=x^2-6x$
Complete the square:
$f(x)=x^2-6x+9-9=(x-3)^2-9$
We start graphing with the basic function $a(x)=x^2$.
We horizontally shift $a(x)$ by 3 units to the right to get $b(x)=(x-3)^2$.
Then we vertically shift $b(x)$ 9 units downwards to get $f(x)=(x-3)^2-9$.
We use 3 points: $(-1,7),(3,-9),(7,7)$
