QUADRATIC EQUATIONS: An Online Treasure for 2nd Year
High School (Mathematics)
Authored by M. Amorin and P. Arinto
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 sure to help each other answer
the questions and understand the basics of quadratic equations.
Questions
 What is the standard form of a quadratric equation?
 What are the ways of finding the roots of a quadratic equation?
 Solve for the roots in x^{2} – 5x + 6 = 0 by factoring.
 Using the method of completing the square, what are the values of x in
x^{2} + 2x = 1?
 What are the possible values of x in x^{2} = 225 using the method called
extracting square roots?
 What are the roots of a quadratic equation x^{2} + 3x – 10 = 0 by the use of a
quadratic formula?
 In an equation x^{2} + 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://wwwgroups.dcs.stand.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/mrquadr.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.
