Detective Descartes

Figure out the secret formula that fits the clues.

Try it out!

select difficulty:

find the equation for a line:

y = x +
y = (x − )² +
y = sin(x + ) +


I made this as a practice tool for a high school student that I'm tutoring. The hope is to build an intuition for how different types of graphs are transformed, and an ability to logically deduce things about a function in a non-predetermined manner based on certain properties. Regrettably, these kind of lateral thinking skills are not always taught, and it's why students can struggle so much in this infamous stage of math education.

Unfortunately, there's still a bug in this current version of the game: you can encounter certain ambiguous cases in the higher levels of quadratics. Specifically, if you know the height of the vertex and two other points on the curve, there may be two possibilities for what the equation is, and the game will only accept one. Before I published the game, I spent hours completely refactoring the code to fix this, by making it check your solution for whether every clue is satisfied, rather than just whether it matches the intended solution - but then I lost all that work from an errant website backup. Ah well, I'll get back to it at some point.

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