How to sketch graph of f(x)=x^3-7x^2+15x-9

Answer 1

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.