# Q to the Power of Two:

The Quintessence of Quadratics

This exploratory project uses a variety of contexts—projectile motion, areas and volumes, the Pythagorean theorem, and economics—to develop students’ understanding of quadratic functions and their representations, as well as methods for solving quadratic equations.

The central problem involves a rocket used to launch a fireworks display. The height of the rocket is described by a quadratic function, and the questions involve vertices and x-intercepts, which are fundamental features of the graphs of quadratic functions.

Over the course of the project, students strengthen their abilities to work with algebraic symbols and to relate algebraic representations to problem situations. Specifically, they see that rewriting quadratic expressions in special ways, either in factored form or in vertex form, provides insight into the graphs of the corresponding functions. Establishing this connection between algebra and geometry is a primary goal of the unit.

**Enduring Understanding**

- Students will develop a better understanding of the inter-relationships between geometry and algebra.
- Students will learn how quadratic equations can be used to solve real-world problems.

**Essential Questions**

- What is a quadratic equation?
- How are mathematical models created and used?

**Execution**

This is an exploratory-based project (a series of guided activities) that culminates in the students designing and programming a projectile-based game.