# What are the real life applications of quadratic forms?

What are the real life applications of quadratic forms? I have used them to sketch conics but are there any other applications?

Among other things, some of which are mentioned in the other answers, you can use them to determine the character of stationary points. If you have a function $f:\mathbb{R}^n\longmapsto\mathbb{R}$, and find points where $\nabla f=0$, then the quadratic form tells you whether it is a saddle point, a min or a max.
Just an example: you can understand the conjugate gradient algorithm for solving the linear system $Ax=b$ with $A$ symmetric and positive definite also by way of minimising the bilinear form $\frac12 x^TAx-b^tx$. This has no implication on the algorithm itself, but gives you more insight into what's going on inside (see e.g. http://www.math.nyu.edu/faculty/greengar/painless-conjugate-gradient.pdf). This "dual" view, i.e. solving a linear system vs. minimising a quadratic form, can also be found often in the theory of Galerkin methods for elliptic PDEs.