factored form provides the best information for graphing by hand ...y = (x – 2)^3 – 6(x – 2)^2 + 9(x – 2)
$y = (x-2)[(x-2)^2 - 6(x-2) + 9]$
$y = (x-2)[(x-2)-3]^2$
$y = (x-2)(x-5)^2$
single zero at x = 2, zero of multiplicity two at x = 5 ... a "bounce" in the graph at (5,0).
End behavior of a cubic function with a positive leading coefficient is $y \to \pm \infty$ as $x \to \pm \infty$
you may also see this as a composite function ...y = (x – 2)^3 – 6(x – 2)^2 + 9(x – 2)
$f(x) = x^3-6x^2+9x = x(x-3)^2$ ... single root at x=0 and double root at x=3
$g(x) = x-2$
$f[g(x)] = f(x-2) = (x-2)[(x-2)-3]^2 = (x-2)(x-5)^2$ the graph of $f$ shifted horizontally 2 units to the right.
link has a good explanation for sketching ...
Algebra - Graphing Polynomials