In this culminating lesson, students synthesize methods of solving quadratic equations and graphing quadratic functions to answer questions about quadratic functions within a context. They use tools learned throughout this unit to grapple with solving problems about a quadratic function that represents a context, and finding the points of intersection of a parabola and a line. Since this work requires using what students know to tackle an unfamiliar problem, students need to make sense of problems and demonstrate perseverance (MP1).

The lesson consists of two substantial problems. All students may attempt both problems. Students with different approaches will then be selected to share their solution with the class. Alternatively, students may choose one of the two problems and prepare a visual display of their solution, conducting a gallery walk or a group presentation at the end of the lesson.

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.