# Lesson 24

Using Quadratic Equations to Model Situations and Solve Problems

### Lesson Narrative

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, without scaffolding, 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. You might decide to have all students attempt both problems and select students with different approaches to share their solution with the class. Alternatively, you might allow students to 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.

### Learning Goals

Teacher Facing

• Choose and write the appropriate form for expressing a quadratic function to solve a problem.
• Interpret features of graphs and expressions that represent quadratic functions to gain information about the situations being modeled.

### Student Facing

• Let’s analyze a situation modeled by a quadratic equation.

### Required Preparation

The tools for creating a visual display and sticky notes are only required if you are doing the suggested gallery walk in the lesson synthesis.

### Student Facing

• I can interpret information about a quadratic function given its equation or a graph.
• I can rewrite quadratic functions in different but equivalent forms of my choosing and use that form to solve problems.
• In situations modeled by quadratic functions, I can decide which form to use depending on the questions being asked.

Building On