Hello, plasticfang!
Quadratic functions may have two, one or no real zeros,
but every cubic function must have at least one real zero. Explain.
A zero of a function is where its graph crosses the xaxis (xintercept).
A quadratic function, , is a parabola.
It can open upward or downward,
. . and can cross the xaxis 0, 1, or 2 times. Code:
  
* *  
  
 * * * * 
 * *  
 * *  * * * *
 *  * * 
  * *  * *
+ +* +**
   * *
   *
  
A cubic function has a range from to .
Its graph extends from the upperleft to the lowerright,
. . or the lowerleft to the upperright.
In either case, it will cross the xaxis at least once. Code:

 *


+**
* *
*  * *
 * *
*  *


* 

We can, of course, draw the horizontal xaxis anywhere.