\(y = x^2 + a\) represents a translation parallel to the \(y\)-axis of the graph of \(y = x^2\). If \(a\) is positive, the graph translates upwards. If \(a\) is negative, the graph translates ...

If \(f(x) = x^2\), then \(af(x) = a(x^2)\). This tells us that we need to multiply each of the \(y\) coordinates on the graph by \(a\) in order to stretch the original graph. Looking at some ...

The field of model checking has evolved into a fundamental technique for verifying the correctness of software and hardware systems. At its core, model checking systematically explores the state space ...

Anyone who’s taken classes in geometry, algebra, trigonometry or other advanced math forms has certainly encountered the graphing calculator before. These multi-function devices make incredibly ...