A cubic graph is any graph which has an \(\text{x}^3\) in its equation. Cubic graphs are still curved but can have more than one change of direction in them.
A quadratic graph is produced when you have an equation of the form \(y = ax^2 + bx + c\), where \(b\) and \(c\) can be zero but \(a\) cannot be zero. All quadratic graphs have a line of symmetry.