The document discusses three forms of quadratic functions - standard form, vertex form, and intercept form - and provides examples of how to write quadratic functions in each form and the steps to graph each by finding the vertex, axis of symmetry, and intercepts. The standard form is ax^2 + bx + c, the vertex form is a(x-h)^2 + k, and the intercept form is a(x-p)(x-q), with each using different variables to indicate the features of the parabolic graph.