# What Are Cubic Models in Math?

You use a cubic model when your points seem to lie along a winding, vertical line. The curve on the graph can be almost invisible—or very prominent. Remember, each set of points has its own unique best model.

Because there’s an infinite amount of ways to create a collection of points that can be modeled as a cubic expression, there’s an infinite number of graphs that fit the expression below. The only difference between these graphs is the values of the coefficients $a$, $b$, $c$ and $d$.

### Cubic Model

A cubic model looks like this:

$$f(x)=a{x}^{3}+b{x}^{2}+cx+d$$ |

Here are three graphs that all fit the expression above:

The difference between these graphs is the values for $a$, $b$, $c$ and $d$. Since $a<0$, the graphs all start in the top left.

Here are three more graphs that fit the expression:

Since $a>0$, the graphs all start in the bottom left.