How to create easing functions for animations?

I enjoy animation on the web and like to cut bikes. More recently, there have learned to use the formula easing functions to animate to requestAnimationFrame. And now I was tormented by the question - how exactly do people create these formulas?
If suddenly someone does not understand about what speech, here are two websites dedicated to singam:
1) timotheegroleau.com/Flash/experiments/easing_funct... (in this case, even the designer is)
2) gizma.com/easing
Specifically to some simple quadratic function I can think of and even came up with all sorts of other stuff, playing with numbers, but how people create all sorts of elastic functions I don't understand. Really just someone long and hard to play with the numbers to get for example here is a formula:?
outElasticBig function(t, b, c, d) {
 var ts = (t/=d)*t;
 var tc = ts*t;
 return b+c*(56*tc*ts + -175*ts*ts + 200*tc + -100*ts + 20*t);
}

I do not believe in miracles, this place is all about math, and I either have not studied this at uni, or already forgot :(
September 19th 19 at 00:28
1 answer
September 19th 19 at 00:30
Solution
This is called "interpolation theory". You can start with the Lagrange's interpolation polynomial. Studied in the courses "Mathematical modelirovanie" and "Numerical methods".
Thank you, you are a real magician :) - kenna commented on September 19th 19 at 00:33

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