Module 3 Summary

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Can you identify the shape created by the water in the fountain shown? You worked a lot with water and other projectiles during this module.

 

In this module you investigated the following questions:

• How are quadratic functions used to model and analyze problems of projectile motion?
  
  
• How do the parameters of quadratic functions describe the properties of their graphs?

In this module you learned that when water is sprayed in a single stream, the path it follows is in the shape of a parabola. You also learned that most objects, when projected into the air, have a trajectory shaped like a parabola. You learned to model these trajectories, as well as structures and commercial situations, using a quadratic function.

 

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In Module 3 you learned what a quadratic function is and you explored the two different forms of the quadratic function: vertex form, y = a(x−p)2 + q, and standard form, y = ax2 + bx + c. You developed the ability to convert between the two forms and to answer questions about trajectories and other scenarios.

 

You developed quadratic functions to model problem situations. Your skills and abilities in working with quadratic functions will be expanded in Module 4: Quadratic Equations and Inequalities.

 

The project for this module involved designing a water spray park for a playground. You chose and designed a variety of fountain sprays that children could play in and enjoy. You relied on your creativity and your developing expertise with quadratic functions. You modelled the paths of those sprays and designed their characteristics using quadratic functions.

 

Module 3: Quadratic Functions, Video Summary is a look back at the math you explored. Watch Module 3: Quadratic Functions, Video Summary to review what you learned and to confirm your answers to the module questions.

The following table summarizes the learning outcomes for Module 3. As a review of what you have learned, complete the table by identifying the activities you undertook to address the corresponding outcomes.

 

You can also use the navigation tree to revisit those lessons that you don’t remember well.

 

Save a copy of your completed table in your course folder for review.

 

Outcomes for This Module	Learning Activities in Which I Addressed This Outcome
Analyze quadratic functions of the form y = a(x−p)2 + q and determine the vertex, domain and range, direction of opening, axis of symmetry, and the x- and y-intercepts.
Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph.
Solve problems involving quadratic functions.

In the next module, Quadratic Equations and Inequalities, you will expand on what you have learned about quadratic functions in this module. You will investigate how to factor and solve quadratic equations that, in this module, you could only estimate using a graphing calculator. You will also learn to solve quadratic inequalities. In this module you applied quadratic functions to several different projectiles. However, in Module 4, you will apply the new concepts more to structures.