 At the end of the popular musical Les Misérables, Inspector Javert falls from a bridge in the middle of Paris into the river below. As he falls, he sings...and sings...and sings.

In this lesson, students use quadratic functions to explore the mathematics of how objects fall. How high was Javert’s bridge, how fast was he traveling when he hit the water, and what’s the maximum height from which someone can safely jump?

### Students will

• Create a quadratic equation to model the relationship between the time an object falls and its distance
• For a given time, evaluate the function to determine the height from which an object fell
• Use the changes in quadratic distance to determine a (linear) model for speed vs. time
• For a given time, evaluate the function to determine an object’s speed at impact
• For a given speed, solve an equation to determine the object’s falling time and initial height
• Discuss the maximum height from which someone can safely jump

### Before you begin

Students should be able to distinguish between linear functions (e.g. y = 2x + 4) and non-linear functions (e.g. y = x2). They should also have experience graphing linear functions.