In this episode of Algebra Applications, students explore the following scenario: Scientists use conic sections to map the trajectories of spacecraft in flight. The setting for this episode is a planned future flight to Mars.

The relationship between slope and grade in cycling is explored. Go on a tour of Italy through the mountains of Tuscany and apply students' understanding of slope.

Scientists use conic sections to map the trajectories of spacecraft in flight. The setting for this episode is a planned future flight to Mars. As the ship travels from Earth to Mars, parabolic, circular, and elliptical paths are explored.

The liftoff and pre-orbital path of the rock is described by a parabola. Students explore the properties of parabolas from the standpoint of the parametric equations that describe the horizontal and vertical directions of motion for the rocket.

The path of a rocket orbiting the Earth can be modeled with the equation of a circle. Students explore the quadratic relation and the parametric equations that can be used to model the path of a spacecraft orbiting Earth.

The planets orbiting the sun follow elliptical paths. In fact, the trajectory of a spacecraft traveling to Mars would also be elliptical. Students explore these various ellipses.

The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes.

In this instructional resource, we show the steps in constructing an egg shape. In the process, students learn about using common points of tangency to create smooth curves from two different shapes. This activity can be done with pencil, compass, ruler, and grid paper. 

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.

This is part of a collection of math examples that focus on quadratic expressions, functions, and equations.