Quadratics in Our World

Introduction

Ever wondered how the drawing of a curve has many applications in our everyday life? How about the path followed by a high jumper or a pole vaulter from the ground, over the bar and landing onto the mat? A diver springing off a dive board into a pool?

These paths taken follow the shape of a curve which you will explore in detail under the theme: quadratics. You will explore a few web sites, the vocabulary associated with quadratics and its applications within real life contexts.

 

Task

By the end of the webquest, you as the student should be able to:

  • perceive what the quadratic graph resembles
  • identify areas in real life contexts that reflect the use of quadratic functions
  • identify the generic format of a quadratic equation ax2+bx+c
  • manipulate the variable a,b and c from the generic formula and state its effect on any given graph
  • identify parts of the curve: axis of symmetry, vertex(minimum and maximum), x and y-intercepts
Process

Activity 1

Write out all you know about quadratics. It can be in the form of a poem, a drawing or definitions

 

Activity 2 -Learning the Language of Quadratics

Find out the definition of the following terms:

  1. axis
  2. symmetry
  3. vertex
  4. minimum value
  5. maximum value
  6. x-intercept
  7. y-intercept

The following sites below will assist you with getting clarity for the terms:

http://www.coolmath.com/reference/online-math-dictionary.html

http://www.mathsisfun.com/algebra/quadratic-equation.html

 

 

Activity 3-Real World Applications of Quadratics

Explore the following site below. It gives great insight into the real world applications of quadratic functions:

http://www.mathwarehouse.com/geometry/parabola/real-world-application.php

 

Using pictures/visuals, write out 6 applications of quadratics in real life situations

 

1.____________________________________________________________________________

 

2.____________________________________________________________________________

 

3.____________________________________________________________________________

 

5.____________________________________________________________________________

 

6.____________________________________________________________________________

 

Activity 5-Problem Set: Obtaining Quadratic Expressions and Equations from Problem Contexts

1. The width of a rectangular field is w yards. The length is 6 yards more than twice the width. Write an algebraic expression for

  • the length of the field
  • the area field

 

 

 

2. The floor of a room is in the shape of a rectangle. The room is c yards long. The width of room is 2 yards less than its width. State in terms of c:

  • the width of the floor
  • the area of the floor

 

 

 

3. In the diagram below, not drawn to scale, AKLM and ASTJ are both rectangles

Given that AS = (3x) cm, AJ = (2x) cm, SK = 3 cm, and JM = 5 cm

i. Obtain an expression in terms of x for the area of the rectangle AKLM               

                       

  

    

 

 

     S 

 K                                                L

           A             J                                M

 

Evaluation

Below shows how your work will be evaluated:

Collaborative Effort -- Each student is graded based on the work done as a group.

1 point - Student did not work with the group.
2 points - Student barely participated in the group.
3 points - Student gave a few helpful hints.
4 points - Student made contributions that were valid to the information being researched.

Use of Online resources:

1 point – Students used no online resources
2 points - Students used a few online resources
3 points - Students used the online resources prescribed only.
4 points - Students used many other resources in addition to those prescribed.

Written Work: 

1 point – Students copied information word for word from the websites
2 points - Students tried to write information in own words                                           

3 points - Students wrote work in own words showing comprehension but did not use pictures and diagrams
4 points - Students wrote work in their own words and used diagrams and pictures to represent work.

 

 

 

Conclusion

You have just explored the application of quadratics in real life contexts and how it can be identified. As a follow up to this we will be

looking at solving actual quadratic equations, manipulating graphs, and further applications of those equations and how they can be

solved. I hope you enjoyed this "Quad-quest!"

Credits

Value is given to the owners of the stated website for uploading as well as the sites embedded within this quest. The contents of this can be shared with users who are willing to use this.

Teacher Page

Created by J.Giffard