A quadratic function is written like this:

Theory

 $f\left(x\right)=a{x}^{2}+bx+c$

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.