How should pharmaceutical companies decide which drugs to develop? There are plenty of medications for conditions like seasonal allergies and athlete’s foot, but treatments for critical conditions such as Ebola are often non-existent. Even though treatments like these may be more important, they’re also less profitable for drug companies.

In this lesson, students create linear and quadratic functions to explore how much pharmaceutical companies profit from different drugs and consider ways to incentivize companies to prioritize medications that are valuable to society.

### Students will

• Given a linear graph, find and interpret the meaning of the y-intercept, x-intercept, slope, and equation
• Evaluate a linear function
• Write, graph, and interpret quadratic functions

### Before you begin

Students should be able to write a linear equation given a graph, and interpret the slope as a unit rate in context, e.g. “the number of additional people who will opt not to buy a drug for every dollar that its price increases.” In addition to linear functions, the lesson also includes quadratic functions. A prior understanding of quadratics is helpful but is not necessary. In fact, the lesson could be used to introduce quadratic functions, and in particular as the product of two linear functions.