Is there a trick to drawing cubic equation graphs?

Question

This year I started drawing out cubic graphs on graph paper...My teacher have been giving a ton of practices.However,I find that it is very difficult to connect the points of the graph,especially the curves... So,is there a trick to drawing out on graph paper easily? Oh,is the french curve or curve ruler easier to draw cubic graphs?

Answer 1

It's better to locate the point of inflection first:

Say for a graph of $f(x)=ax^3+bx^2+cx+d$,

$$f''\left( -\frac{b}{3a} \right)=0$$

The graph has a rotation symmetry about the point of inflection namely $$\left( -\frac{b}{3a}, d-\frac{bc}{3a}+\frac{2b^3}{27a^2} \right)$$