Equation for a quadratic curve in a three-dimensional space?

I'm not really sure if this is the right area BUT I did similar things such as this in trig so I thought this might be a good place to ask.

I'm working within a three dimensional space and I have three points that I must create a quadratic curve out of. The curve must touch all three points. In 2d the process for solving this is easy enough but in three dimensions I begin to have trouble. I built a script that can find and output the X,Y,and Z coordinates and their distance in relation to each other but I need to know a formula (or possibly two combining formulas. I'm not really sure how using two would work for programming) to plug in the values. Anyone know a formula like this?