The task challenges a student to demonstrate an understanding of quadratic functions in various forms. A student must make sense of the meaning of relations and functions and select, convert flexibly among, and use various representations for them. A student must be able to approximate and interpret rates of change from graphic and numeric data. A student must be able to identify minimum point and solutions of a quadratic. A student must determine the solutions to a quadratic equation by using algebra.
This lesson unit is intended to help you assess how well students are able to understand what the different algebraic forms of a quadratic function reveal about the properties of its graphical representation. In particular, the lesson will help you identify and help students who have the following difficulties:
• Understanding how the factored form of the function can identify a graph’s roots.
• Understanding how the completed square form of the function can identify a graph’s maximum or minimum point.
• Understanding how the standard form of the function can identify a graph’s intercept.