The diagram above shows three typical forms for constructing correspondence rules that describe quadratic functions: - The Vertex Form, which is convenient to use when you have information about the vertex or when you want to emphasize such information. You can explore this form with the Graph transformations: the Vertex Form activity. - The Polynomial Form, which presents the functions as a sum of three basic components. You can explore this form with the Addition of functions: the Polynomial Form activity. - The Product Form, which is convenient to use when you have information about the roots or when you want to emphasize such information. You can explore this form with the Products of linear functions activity. But you can write quadratic functions in other forms, in addition to these three common ones. This activity introduces the various forms for constructing correspondece rules for quadratic functions and highlights the pros and cons of the various forms from the point of view of the information that each form reveals about the function. Since each form has its advantages, it is often useful to switch from one to another. The present activity helps you do that. Prepare a summary on switching between different forms of correspondence rules for quadratic functions Give examples of switching from one form of a correspondence rule to another one that describes the same function. Describe ideas that help you switch from one form to another. Did you use algebraic operations? Graphs? Value tables? If you discovered the correspondence rule of one form for which you could not find an equivalent correspondence rule of a different form, bring examples and explain the problematic points. Can you describe general methods of switching from one form of correspondence rule to another? What are the advantages of different forms of correspondence rules from the point of view of the information each one reveals about the function?

Vertex Form Polynomial Form Product Form Reading information about functions Immunization against the common cold Numeric surprises Constructing functions Wage increase Partial pictures Examining value tables Families of functions Vertex paths Family and sub-families Parametric families Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6 Exercise 7 Exercise 8 Exercise 9 Exercise 10 Exercise 11 Exercise 12