MAT 1033C – INTERMEDIATE ALGEBRA Liudmila Kashirskaya lkashirskaya@mail.valenciacollege.edu http://frontdoor.valenciacollege.edu/? lkashirskaya

Why Do I Love Math? Learn 3 Simple Reasons Why You Should Love It Too 1. Mathematics requires a different level of thinking - You become a problem solver in this world. But before we can solve these problems, we need to understand them and come up with for its best solution.  2.  Math is really fun: you are given problems in real life like buying and selling.  Learning Math is really fun. New ideas every time. There is joy for everyone. Solving problems satisfies. I am glad, you are glad when our answers are all right. We may feel that we are bright. Mathematics makes us wise. 3. Mathematics is life.  We are not using formulas and we are not using variables like x and y everyday, but we always face situations like we need to make decisions, analyze and weigh things regarding its relevance. All of these things are related to Mathematics.

Facts from History Solutions to problems equivalent to the quadratic equation were known as early as 2000 BC. With a purely geometric approach Pythagoras and Euclid created a general procedure to find solutions of the quadratic equation. In his work Arithmetica, the Greek mathematician Diophantus solved the quadratic equation, but giving only one root, even when both roots were positive. Image source: galleryhip.com

The further development of algebra was the general algebraic solution of the cubic and quartic equations, developed in the mid-16th century. The idea of a determinant was developed by Japanese mathematician Seki Kōwa in the 17th century, followed independently by Gottfried Leibniz ten years later, for the purpose of solving systems of simultaneous linear equations using matrices.

Image source: galleryhip.com

The simplest parabola

Which images have to do with quadratic equations? Image source: Wikimedia commons

All of them!

Quadratic equations describe these common shapes Image source: jwilson.coe.uga.edu

We owe advances in astronomy, modern communication, entertainment, and even shaving mirrors to quadratic equations! Image source: Wikimedia commons

Planets go around the sun in elliptical orbits – also described by quadratic equations Image source: Wikimedia commons, NASA

Al·ge·bra - Definition The part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations. Algebra (from Arabic "al-jabr" meaning "reunion of broken parts"[1]) is one of the broad parts of mathematics. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.

  In arithmetic, only numbers and their arithmetical operations (such as +, −, ×, ÷) occur. In Algebra, numbers are often represented by symbols called variables (such as a, n, x, y or z). 

MAT 1033C – INTERMEDIATE ALGEBRA

Intermediate Algebra presents algebraic skills for MAC 1105 Intermediate Algebra presents algebraic skills for MAC 1105. Topics include linear equations and inequalities in two variables and their graphs, systems of linear equations and inequalities, introduction to functions, factoring, algebraic fractions, rational equations, radicals and rational exponents, complex numbers, quadratic equations, scientific notation, applications of the above topics and the communication of mathematics.

1.5 Introduction to Graphing Computers, the Internet are creating large amounts of data. To make the conclusion we have to analyzed data. Tuition and Fees at Public Colleges Year 2000 2005 2010 2015 Cost $4845 $6708 $8351 $9410 The ordered pair (x, y) represents a relation. Relation is a set of ordered pairs. This relation can be represented by a set S= 2000, 4845 , 2005,6708 , 2010,8351 , 2015,9410 The set of all x-values is called the domain: D = {2000, 2005, 2010, 2015} The set of all y-values is called the range: R= { 4845, 6708, 8351, 9410}

Example1: Find the domain and range for the relation S given by S={(-2,3),(-2,4),(5,4)} Solution The domain of S is D={-2,5} And the range of S is R={3,4}

Example 2: The formula P=662x calculates the number of pages P that the average Facebook visitor views in x months. Give four ordered pairs in the relation. Answer: (0,0), (1,662), (2,1324), (3,1986)

The Cartesian Coordinate System We can use the Cartesian Coordinate System on xy-plane to graph a relation. Two axes divide the xy –plane into four regions – quadrants. Quadrant IV (+, -)

Plotting points Example 3: Plot the data listed in the table: x -2 3 5 3 5 y -1 4

Example 4: Use the graph to determine the domain and range of the relation.

Creating Line Graphs Exercise: 1 2 3 y -4 -1 5 S=? D=? R=?