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Completing the Square for Vertex Form

Explore how rewriting a quadratic expression reveals key features of its graph.

Task 1

Putting It All Together

Answer these open ended questions on your own or with others to form deeper math connections.

Task 2

What can you tell about the graph of given its equation ? What else can you tell about the graph if the equation is rewritten as ?

Task 3

What are some characteristics you can interpret about any quadratic function that is written in the form ?

Task 4

How does the process of completing the square help you gather information about the graph of a quadratic function?