Reading a graph and its transformations
Working out what a function is, and what was done to it, from where the picture ended up.
A worked example
A parabola has its lowest point at (2, -3).\n\nIn y = a(x - h)² + k the vertex is (h, k), so h = 2 and k = -3, giving y = (x - 2)² - 3.\n\nThe minimum VALUE is -3. The 2 is where the minimum happens, not what it is — a distinction the wording of a diploma question turns on.
The mistake people actually make
The sign inside the bracket. (x - 2) shifts the graph two to the RIGHT, not left, because the bracket is zero when x is 2. And the sign of the squared term is the only thing that decides which way a parabola opens: shifting a graph downward moves it without ever turning it over.