There are few features that you can use to sketch any polynomial function
First is to find x-intercepts of that polynomial. x-intercepts are positions x axis at which function f(x) is equal to 0
Second feature is to find first derivative of the function f(x), make it equal to 0 and again find x values that make first derivative equal to 0. after that implement those x values in f(x) to find f(x) for those values. Now you have sets of (x,y) which are local minimum and maximums of polynomail. Knowing these and with a bit of calculation you can make a decent skecth of any polynomial.
