Created by J.Giffard
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:
- axis
- symmetry
- vertex
- minimum value
- maximum value
- x-intercept
- y-intercept
The following sites below will assist you with getting clarity for the terms:
http://www.mathsisfun.com/algebra/quadratic-equation.html
http://www.coolmath.com/reference/online-math-dictionary.html
Activity 3-Real World Applications of Quadratics
Explore the following sites below. They give great insight into the real world applications of quadratic functions:
http://www.mathwarehouse.com/geometry/parabola/real-world-application.php
http://carondelet.net/Family/Math/03210/page4.htm
https://answers.yahoo.com/question/index?qid=20080622160214AA4lux8
http://www.learner.org/workshops/algebra/workshop4/index.html
Using pictures/visuals, write out 6 applications of quadratics in real life situations:
1.____________________________________________________________________________
2.____________________________________________________________________________
3.____________________________________________________________________________
4.____________________________________________________________________________
5.____________________________________________________________________________
6.____________________________________________________________________________
Activity 4-The Format of a quadratic formula
Using: https://www.desmos.com/calculator/icqxxufsb6, change the values of a, b and c to observe the effect of a on the graph, the effect of b on the graph and the effect of c on the graph.
Write a statement below for the following:
1. When a increases on the graph__________________________________________________________________________
2. When a decreases on the graph_________________________________________________________________________
3. When b increases on the graph__________________________________________________________________________
4.When b decreases on the graph__________________________________________________________________________
5. When c increases on the graph__________________________________________________________________________
6. When c decreases on the graph__________________________________________________________________________
Activity 5-Problem Set: Obtaining Quadratic Expressions and Equations from Problem Contexts
1. The width of a rectangular field is w metres. The length is 6 metres more than twice the width. Write in terms of 1, 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 metres long. The width of room is 2 metres less than its width. State in terms of c:
- the width of the floor
- the area of the floor
3. If each side of a square is increased by 3cm, its area is increased by 45cm2. Write an equation to represent the information given.
4. In the diagram below, not drawn to scale, AKLM and ASTJ are both rectangles
|
S |
K L
A J M |
Given that AS=3xcm, AJ=2x cm,SK= 3cm and JM=5cm
i. Obtain an expression in terms of x for the area of the rectangle AKLM
ii. Given that the area of the rectangle AKLM is 60 cm2, show that 2x2+7x-15=0
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 not using pictures and diagrams
4 points - Students wrote work in their own words using visuals to present work using diagrams and pictures
Oral Presentation
1 point – Student and group members showed little preparation
2 points - Student and members prepared the information but was unsure of themselves when presenting
3 points - Student and group members presented the information well
4 points - Student and other group members presented the information with confidence and showed an understanding of the content.
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 the actual quadratic equations manipulating graphs and further applications of those equations and how they can be solved. I hope you enjoyed this "Quad-quest". Journey on into the quadratic maze as you continue to learn more about quadratics!
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.