Quadratic approximations

How to approximate a multivariable function with a quadratic function. This is analogous to a quadratic Taylor polynomial in single-variable calculus.

What do quadratic approximations look like

Quadratic approximation formula, part 1

Quadratic approximation formula, part 2

Quadratic approximation example

The Hessian matrix

The Hessian matrix

Expressing a quadratic form with a matrix

Vector form of multivariable quadratic approximation