Lesson
Case Study #1
To complete this exercise you may work on your own or with a partner at your teacher's direction. The analysis used will require you to
- model a real problem
- use the quadratic formula to find the roots of a quadratic equation
- use the discriminant to predict the nature of the roots
- write the quadratic equation as a function and change it to its transformational form
- check x-intercepts of a quadratic graph
- use transformational techniques to graph the quadratic function
- research a well known mathematical topic - golden section - and its applications. Check the internet ; especially if your library facilities are limited.
Case Study #2
To complete this exercise you may work on your own or with a partner at your teacher's direction. The analysis used will require you to
- find the roots of a quadratic equation and relate these to the x-intercepts of the corresponding quadratic function
- indicate the maximum or minimum y-value for a parabola
- determine the equation from given information
- determine the transformational form of a quadratic function
- use regression to find a quadratic relationship
- examine the sum and product of the roots with respect to the quadratic equation
Case Study #3
To complete this exercise you may work on your own or with a partner at your teacher's direction. The analysis used will require you to
- use growth patterns that are linear, quadratic and/or higher-power functions
- distinguish between these patterns
- model real-world quadratic relationships
- use the quadratic formula
- use roots to determine the number and location of the
x-intercepts of a quadratic function
Activity
These items may be used by your teacher as items for:
- a portfolio item
- as a homework project as part of an end of chapter review
- as a quiz item or test item
Check with your teacher for further instructions!
Test Yourself
Discuss issues surrounding these case studies/extension with your teacher and on/or classmates.