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If we include to Linear Discriminant Analysis quadratic parameters we get Quadratic Discriminant Analysis classifier. Number of parameters is $(K-1)\times[(p\times(p+3)/2) + 1]$ where K is number of classes and p is number of features.

Why $K-1$? In the book it is said that we only need to compare $\delta_{k}(x) - \delta_{K}(x)$ of discriminant functions of some prespecified class K, but why do we do that and how it works?

$(p\times(p+3)/2) + 1$ is number of factors in multivariate quadratic function how is it calculated?

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