A cubic function is one in the form *f*(*x*) = *ax*^{3} + *bx*^{2} + *cx* + *d*.

The "basic" cubic function, *f*(*x*) = *x*^{3}, is graphed below.

The function of the coefficient *a* in the general equation is to make the graph "wider" or "skinnier", or to reflect it (if negative):

The constant *d* in the equation is the *y*-intercept of the graph.

The effects of *b* and *c* on the graph are more complicated. However, if you can factor the right side of the equation, you can find one or more *x*-intercepts, and use these to sketch the graph. (Some cubics, however, cannot be factored.)

A cubic function may have one, two or three *x*-intercepts, corresponding to the real roots of the related cubic equation.