Function Transformations Applet

The intended use for this application is for students to investigate the different transformations of the graph of the function g(x) = x^2. Click on the sliders to change each of the 3 parameters a, b, and c on the graph of f(x) = a (x + b)^2 + c, and observe what happens to the graph.
Can you find an equation that correspond to a reflection on the x- axis of the graph of g(x) = x^2?
What causes the graph of f(x) to be shifted to the left or to the right?
What causes the graph of f(x) to be shifted vertically?

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Rocio Franklin, Created with GeoGebra