#quadratic-boundary

Both an SVM with a quadratic (degree-2 polynomial) kernel and a classifier with one unrestricted Gaussian per class produce decision rules of the form $\mathrm{sign}(a x_1^2 + b x_1 x_2 + c x_2^2 + d x_1 + e x_2 + f)$ on $\mathbb{R}^2$. What is the VC dimension of the set of all such rules?