Transformations of the Graphs of Functions

The graph of the function x^2 is a parabola as shown. The vertex is (0,0). But not all parabolas have a vertex at the origin, not all parabolas are the same width and not all parabolas open up. What determines the vertex, how wide or narrow it is and if it opens up or down?
Using the general equation of a parabola can you discover the transformations based on the coeffecients (A, B, C) in the equation?
f(x) = A(x+B)^2 + C

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Explore transformations of the graph of f(x).
1. As you change the values of A, B, and C what happens to the graph of the function?
2. How does a positive value for A affect the graph of f(x)?
How does a negative value for A affect the graph of f(x)?
3. Describe the change in the graph as A approaches 0 from 3?
4. Negative values of B have what affect on the graph of f(x)?
Positive values of B have what affect on the graph of f(x)?
5. What do you predict will happen as you change the value of C?
6. How does the graph shift for positive values of C?
How does the graph shift for negative values of C?
7. Will the transformations be the same for the graph of f(x) = x^3?

Tammy Short, Created with GeoGebra