For a proper Fourier transform you need to wait until the first years of the university, perhaps the lasts year of secondary school in some places. Anyway, it doesn't look like a nice function for a Fourier transform, because the border effect will be huge.

In the middle of secondary school, if you are lucky you can try fitting the function line a polinomial plus a trigonometric function with Excel. You have to pick an initial value of the parameters that is close to the function, otherwise solver will never get a good fit.

I'm not sure how many math teacher are prepared for this. I have more faith in physics teachers that have a better training in dealing with noisy real word functions that have to be fitted to a model.

> see if the second derivative means we're all gonna die,

I think that even the worst model don't predict the humanity extinction, perhaps a huge amount of displacement and the following wars, problem for crops and food production and the following hunger, change of rain pattern, sea level increase, and other very nasty stuff, but not extinction. Also, the timeframe of most of the catastrophes is more than a century, so there is plenty of time to dance on the Titanic.