Transformations of Functions: Using Parent Functions to Sketch Graphs

We walk through a process for graphing a shifted, scaled parabola f(x) = 3(x-2)^2 - 3.14159.
(a) the (x-2)^2 introduces a shift to the RIGHT of the parent function f(x) = x^2. This is because x = 2 now plays the role that x=0 would in the parent funciton.
(b) the factor of positive 3 makes the parabola continue to open upward, but it rises faster. The parabola becomes narrowed due to the coefficient of positive 3.
(c) the subtraction of "pi" simply shifts the entire graph downward by 3.14159 units. #precalculus #math #functions