Quadratic functions and hyperbolic cosine functions are very different functions and have very different properties. However, to an naked eye their graphs are similar. Is there any tip to quickly tell them apart?
2026-03-26 12:36:32.1774528592
How to tell the difference between a quadratic curve and a hyperbolic cosine curve?
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The simple answer is, you can't, at least at small scales. (That's because the polynomial is the first few terms of the Taylor series for the cosh function, so it's going to be a good approximation.)
Try googling "y = cosh x, y= 1 + x^2" and you will see the graphs superimposed. They are nearly indistinguishable close to the origin, at least to the naked eye.
But note as you get further out from the origin, the cosh curve is asymptotically exponential, which increases much faster than any polynomial.