When viewed within the realm of dynamical systems, the humble quadratic function reveals some fascinating behavior. To explore this behavior, the quadratic function Q^c(x) = x2 + c is applied to an initial point x_o. This process is iterated using composition. The result is a sequence of numbers, {Q_c(xo), Q²_cxo), Q³_c(xo),…}, which can exhibit widely varying behavior depending on the choice of the constant c. More precisely, the sequence can approach a limiting value or display periodicity. For some values of c, chaotic behavior is found. Cobweb and orbit diagrams provide the tools for visualization. A collection of these diagrams will be presented along with background information.