Transformations of the Quadratic Function

Objective:
In this applet you will explore transformations of the quadratic function. You will be exploring the function g(x)=a(x-h)^2+k by investigating the roles of a,h, and k in the graph of the function.

Instructions:
In order to investigate the roles of a,h, and h you will need to use the sliders provided below.
The red slider allows you to change the value of 'a', the allows you to change the value of 'h', and the green slider allows you to change the value of 'k'. As you click on each colored point and drag it from left to right, you will observe that as the value of a, h and k change, the graph of the function also changes.

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Some questions to consider:

1. How does changing 'a' affect the graph? What happens when 'a' is negative?
2. What role does 'h' play in transforming the graph?
3. What role does 'k' play in transforming the graph?

S. Michel, Created with GeoGebra