The Best Jump Algorithm?

Who's up for a bit of challenge or provide some tips or better code?
I'm having trouble with the math side of doing jumps on the game I'm making.
Can someone please help me out for a while?
My character's jump looks weird, it looks pointy.
There's code here http://codepad.org/SXH4ydz8 where we can start.
There are constraints there.

Make a proper Physics simulation and just give your Entity an upward force of X newtons which will cause it to rise into the air and then eventually fall back in a nice smooth pattern due to gravity.