At this model demonstrates a different number of roots of an equation depend on the equation parameter. Consider equation 2(x11)^{2}1=a. To investigate a number of its roots see stepbystep construction of f(x) = 2(x11)^{2}1 graph. Consequent transformations are x^{2}, then to (x1)^{2}, then to (x1)^{2}, then to (x11)^{2}, then to 2(x11)^{2}, then to 2(x11)^{2}1, and finally to 2(x11)^{2}1. depending on a construct stepbystep a graph of f(x) = 2(x11)^{2}1. Transform x^{2} to (x1)^{2} to (x1)^{2} to (x11)^{2} to 2(x11)^{2} to 2(x11)^{2}1 and finally to 2(x11)^{2}1. Now draw various horizontal lines. A cross point of a line and the graph is a root of the equation. Note that different lines may have different number of cross points (roots of the equation). At this manner there is no roots for negative a, 2 roots for a>1, 4 roots for a=0, 5 roots for a=1 and 8 roots are for 0<a<1. The model is a movie. To navigate through the movie use Play, Pause, Stop, Previous step and Next step buttons.
