Richard Gonzalez found my triplot.R function and enhanced it by adding a graphical user interface. By the use of sliders, one can change the beta parameters a and b, the data values s and f, and see the effect of the changes on the triplot (prior, likelihood, and posterior) and the predictive distribution.
Here are a couple of illustrations.
In the first example, the prior is beta(3, 7) and one observes 6 successes and 14 failures. The prior information is consistent with the data information and the observed number of successes is in the middle of the predictive distribution.
In the second example, the beta(6, 2) prior is in conflict with the data (s=6, f=14) and the observed number of successes is in the tail of the predictive distribution.