Representing quadratic functions graphically

This resource develops the concept of what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. Particular attention is paid to:

• How the factored form of the function can identify a graph’s roots.
• How the completed square form of the function can identify a graph’s maximum or minimum point.
• How the standard form of the function can identify a graph’s intercept.

Students initially consider a quadratic in; standard form, factored form, and completed square form. The first task is to use the different forms to identify key coordinates of a key feature of each of their graphs.

The main activity is a ‘domino’ matching exercise where cards are presented with a quadratic function in different forms must be matched with a graphical representation showing the key features of the function. Some cards have blanks and require students to complete the information.  

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.