## Demo

### Partial Derivatives

This demo lets you study a family of quadratic functions $$f(x,y) = \frac{1}{2}(ax^2 + 2bxy + cy^2)$$. Recall that we can determine which of the 6 equivalence classes $$f$$ belongs by the sign of the discriminant $$\Delta = ac - b^2$$ and the sign of $$a$$.