Sketch y = 9x – 4x^3, showing where the curve crosses the x axis.

First you should look at the equation and try and get a sense of the general shape of the graph. The highest power in here is a 3, so this is a cubic graph. The coefficient (number in front of the x^3) is a negative, so it will be a negative cubic graph (draw what this looks like.) Next, we need to figure out where the curve intersects the x axis. To do this, we will first factorise the equation to make it simpler to understand (spot the difference of 2 squares in the factorisation), and then find all values of x when y=0, as this will be the points where the curve cuts the x axis.