Exploring Transformations of Quadratic Equations in Vertex Form

Vertex Form of Quadratic Equations
Explore Transformations of Quadratics
[img]data:image/png;base64,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[/img]is the parent function ( the most basic quadratic function)[br][br]f(x) is the transformed function.[br]Spend 5 minutes changing the a, h, & k values (move the colored sliders).[br] Observe the changes in the graph in order to answer the questions below.
The Effect of Changing the "a" Value
a) What happens to the graph when a is greater than 1?[br][br]b) What happens to the graph when 0 < a < 1 (like .5, .3, or .8) ?[br][br]c) What happens when a is negative?
The Effect of Changing the "h" Value
a) What happens to the graph when h is positive?[br][br]b) What happens to the graph when h is negative?
The Effect of Changing the "k" Value
a) What happens to the graph when k is positive?[br][br]b) What happens to the graph when k is negative?
Close
– kyra burdick, carahaines

Information: Exploring Transformations of Quadratic Equations in Vertex Form