y² = x³ - 432

What do you want me to do with this?  discuss it?

I can see straight away that 

$$x^3-432\ge 0\\
x^3\ge 432\\
\mbox{Hence}\\
x\ge \sqrt[3]{432}$$

I can also see that as x approaches infinity y plus or minus infinity.

I can 'see' that the cuve will be symmetrical about the x axis. (This is the line y=0)

Maybe that is enough discussion.

Here is the graph.