Cubic curve with a point of inflection Not quite what I wanted to ask.  What I really wanted to know is why you can't have a cubic curve that starts from top left and ends top right.
 A: Consider what happens when the value of $x$ is very large positive and very large negative. The $x^3$ term will always be much larger than the other terms if $x$ is large enough. If $x$ is positive the whole expression will evaluate to a large number with the same sign as the coefficient of $x^3$. If $x$ is negative the expression will evaluate to a large number with sign opposite to the coefficient of $x^3$ so.... 
When $x$ is large negative the expression will be at either the bottom left if the coefficient is positive or the top left if the coefficient is negative. 
When $x$ is large positive the expression will be at the top right if the coefficient is positive or at the bottom right if the coefficient is negative.
So a cubic must run either from the bottom left to the top right or from the top left to the bottom right. 
One consequence of this is that, because a cubic describes a smooth continuous curve it must cross the $x$ axis (where $y=0$) at some point, which is a real root. All cubics have at least one real root. Similar arguments apply to any polynomial of odd degree.
