How to sketch graph of f(x)=x^3-7x^2+15x-9
you know the general shape of a cubic. The only real trick is finding where the roots are, then sketch a cubic curve through the roots.
A little synthetic division shows that
f(x) = (x-1)(x-3)(x-3)
So, draw your cubic curve so that it crosses at x=1 and is tangent at x=3.