How do you model quad tweening?

I have been making my own tweening system where I use a specific function to have inputted values from 0 to 1 give out outputs that are 0 to 1 correspondingly. (the y will represent the third input in the lerp.) I want to have that function be of a similar output to a quad function in tweening where the increase in y originally is slow, then speeds up, and finally slows down. I have looked at a few graphs of different functions and the closest I've come is with a cube root function. Any ideas? Here is a link to the different tween functions:

(the quad one is one that I want to resemble) https://www.youtube.com/watch?v=qgGDwTn0zgo (At 4:39 it shows them)