Linear & Quadratic Functions of Two Variables

The general form of a quadratic function of two variables [math]g(x,y)[/math] is [math]g(x,y)=ax^2+by^2+cxy+dx+ey+f[/math]. Explain how varying each of the coefficients [math]a,...,f[/math] varies the shape of the graph of the function [math]g(x,y)[/math]. The general form of a linear function of two variable [math]h(x,y)[/math] is [math]h(x,y)=Ax+By+C[/math]. When plotted this function is a plane. The X, Y, and Z sliders allow you place points on the x, y, and z axes through which the plane passes.