A quadratic function is written like this:
Theory
Here are a couple of examples of the graphs of quadratic functions:
You use the quadratic model when your points lie in a convex or concave arc. But you can also use other polynomial functions in those cases. You can test different polynomial functions to see what gives the best fit.
A typical situation where using a quadratic model for your data points makes sense is when you assume that what you’re modeling has a maximum or minimum. For example, if you want to model a javelin throw, you know that the height of a javelin throw has a maximum. That means a quadratic model would fit the data well.