The document discusses two forms of quadratic equations: standard form (y = ax^2 + bx + c) and vertex form (y = a(x - h)^2 + k). It shows that vertex form can be rewritten as standard form by expanding the expression, with a = a, b = -2ah, and c = ah^2 + k. This allows the vertex (h, k) to be determined directly from the standard form equation by solving for h and k in terms of a, b, and c. An example demonstrates rewriting a vertex form equation into standard form and finding the vertex (-1, -4).