The graph below shows how we can create various quadratic functions by transforming the parent function x^{2} through vertical shift,
horizontal shift and reflection across the x axis. Function 4, represented with purple on the left of the graph is the function -(x+7)^{2} +4 is a composition of 3 successive simple transformations.
The original range will change after each of these transformations, from y E[0, inf] to (-inf, 4].