QUADRATIC EQUATIONS

 

An Online Treasure

for Second Year High School (Mathematics)

 
 
 
Introduction

 

The Wall Street Journal, a famous magazine read by businessmen and people in finance and related fields, is said to have published an article on June 16, 1998, which said the following:

 

... algebra is what teachers call a gatekeeper course; you have to go through it to reach the possibilities beyond. Algebra is

the language of math and science, 'the language of problem solving,' says University of Chicago math professor Zalman Usiskin.

It deals in abstractions—using letters to generalize math operations—that expand thinking skills.

 

That algebra develops abstract thinking skills can be seen in many ways. Algebraic expressions and equations, for example, serve as models for interpreting and making inferences about data.

 

In the previous unit we learned about linear equations. In this activity, we begin learning about another set of equations, called quadratic equations. We will do so by reading some websites that provide an overview of quadratic equations. As you read each website (listed under Resources below), you will look for answers to some questions (also listed below). After answering all of the questions, answer the Big Question.

 

You will do this activity in groups of three. Be usre to help each other answer the questions and understand the basics of quadratic equations.

 

 

Questions

 

1.      What is the standard form of a quadratric equation?

2.      What are the ways of finding the roots of a quadratic equation?

  1. Solve for the roots in x2 – 5x + 6 = 0 by factoring.
  2. Using the method of completing the square, what are the values of x in

x2  + 2x = 1?

  1. What are the possible values of x in x2 = 225 using the method called extracting square roots?
  2. What are the roots of a quadratic equation x2 + 3x – 10 = 0 by the use of a quadratic formula?
  3. In an equation x2 + 3x + 1 = 0, what is the value of the discriminant?

 

 

Resources
 
Definition of a Quadratic Equation

http://mathworld.wolfram.com/QuadraticEquation.html

 

The Standard form of a Quadratic Equation

http://www.math.utah.edu/online/1010/quadeq/

 

Ways of Finding the Roots of a Quadratic Equation

http://mathforum.org/library/drmath/view/62884.html

 

Steps in Finding the Roots of a Quadratic Equation by Factoring

http://www.sparknotes.com/math/algebra2/factoring/section1.html

 

Steps in Finding the Roots of a Quadratic Equation by Completing the Square     

http://www.purplemath.com/modules/sqrquad.htm

 

Finding the Roots of a Quadratic Equation by Extracting Square Roots Quadratic Equations and Parabolas

http://www.algebra.com/algebra/homework/quadratic/

 

History of Algebra and Trigonometry

http://www.pbs.org/empires/islam/innoalgebra.html

http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Quadratic_etc_equations.html

 

Real Life Uses of Quadratic Equations

http://mathforum.org/library/drmath/view/60810.html

http://www.chem.tamu.edu/class/fyp/mathrev/mr-quadr.html

http://www.pbs.org/teachersource/mathline/concepts/designandmath/activity3.shtm

 

 

The Big Question
 
A. Now that you have been introduced to quadratic equations, see if you can represent the problem below in the form of a quadratic equation and then solve it:
 
One of the hotels in Dumaguete City rented a certain number of guest rooms for P30,000. There were 7 more rooms rented when the price was reduced by P30 per room. How many guest rooms were rented?
 
B. In your own words and citing your own example, briefly explain why the study of quadratic equations is important.
 
Write your answers to A and B on a sheet of paper. Remember that you will answer these as a group, not individually. Write the names of group members on your answer sheet. Submit your answer sheet on the next class meeting.
 

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Authored by M. Amorin and P. Arinto