Some functions are easier to work with than others, especially when using computers. Of the different types of functions, polynomials are some of the easiest to work with. Quadratic approximation is a way of approximating a more complicated function as a second-order polynomial. In addition to making sure the first derivative of the approximation at a point is equal to the first derivative of the actual function at that point (which is what you do in linear approximations), quadratic approximations make sure that the second derivative of the approximation at that point matches the second derivative of the function at that point. This leads to a better approximation than simply using linear approximation. Note that the accuracy of the approximation generally goes down the farther away you get from the point where you based the function.
Sources (all Khan Academy):
- https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/quadratic-approximations/v/what-do-quadratic-approximations-look-like
- https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/quadratic-approximations/v/quadratic-approximation-formula-part-1
- https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/quadratic-approximations/v/quadratic-approximation-formula-part-2
- https://www.khanacademy.org/math/multivariable-calculus/applications-of-multivariable-derivatives/quadratic-approximations/v/quadratic-approximation-example
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Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
