Contextualization

The second degree equation, or quadratic equation, is a polynomial function that appears frequently in various real-world applications, from basic physics to economics and finance. It is expressed in the form ax²+bx+c = 0, where a, b, and c are real numbers and 'a' cannot be zero. To solve a second degree equation, we use the Bhaskara's formula, a mathematical equation that allows us to find the roots of the quadratic equation.

The quadratic function and the Bhaskara's formula are essential elements in the study of Mathematics, being necessary for the understanding of a wide range of concepts, such as functions and graphs, study of signs, and optimization problems. Moreover, they have practical applications in many areas of exact and biological sciences, business, and engineering.

Second degree equations are present in problem resolutions involving object launches, area optimization, cost analysis in economics, and even in everyday situations, such as determining the time needed to complete a task, for example. Understanding this mathematical tool is therefore fundamental for all those who wish to have a solid level of mathematical literacy.

Practical Activity: The Drone's Flight

Activity Title: The Drone's Flight - An Adventure in Bashkara

Project Objective

The objective of this project is to apply the knowledge about second degree equations and the Bhaskara's formula to simulate and analyze the trajectory of a drone when launched under certain conditions. The project covers mathematical calculations, principles of physics, and programming skills. Students will work in groups of 3 to 5, and the project will require more than 12 hours from each member to be executed.

Detailed Project Description

Students will divide into groups, and each set will be responsible for simulating the flight of a drone. They will program the drone's trajectory to replicate a parabola, characteristic of second degree equations. Each group will also calculate the maximum height the drone will reach and the time it will take to return to the ground, using the Bhaskara's formula.

In addition, students will have to consider different scenarios, such as changes in the drone's launch speed and external influences, such as wind and air resistance. All these elements must be taken into account when preparing the final report.

Required Materials

1. Knowledge of second degree equations and Bhaskara's Formula.
2. Computer with internet access.
3. Programming software (we suggest Python, due to its simplicity and resources for mathematical calculations).
4. Drone (optional, calculations and simulations can be entirely theoretical).

Detailed Step-by-Step

1. Study the theory of second degree equations and Bhaskara's formula.
2. Choose the programming software and learn the basic commands.
3. Plan the drone's trajectory, predicting the parabola it will describe.
4. Implement the programmed trajectory on the drone.
5. Perform experiments to validate the calculations made.
6. Collect and analyze the data from the experiments.
7. Report elaboration.

Project Deliverables

Students must deliver a detailed report of the entire project development process:

1. Introduction: Contextualization of the problem and motivation for choosing the drone. Relevance of using the second degree equation and Bhaskara's formula in solving this problem.

2. Development: Detailed explanation of the theory of second degree equations and Bhaskara's formula. Description of the activity, including the methodology used to plan and program the drone's trajectory, the experiment carried out, and analysis of the results.

3. Conclusion: Recap of the main points, lessons learned, and conclusions drawn about the project. Students must make it clear how they applied theoretical knowledge in practice and how the project contributed to their learning.

4. Bibliography: List of sources that assisted in the development of the entire project.