What is algebra?
The part of mathematics in which letters and other symbols are used to represent numbers and quantities in formula and equations.
Why is Algebra used in school?
Algebra 2 is used in schools for various reasons.Basic algebra is the first in a series of higher-level math classes students need to succeed in college and life. Because many students fail to develop a solid math foundation, an alarming number of them graduate from high school unprepared for college or work. Many end up taking remedial math in college, which makes getting a degree a longer, costlier process than it is for their more prepared classmates. And it means they're less likely to complete a college-level math course. For middle-schoolers and their parents, the message is clear: It's easier to learn the math now than to relearn it later.
Why do they say Algebra is needed outside of school?
The following is quoted by National Geographic:
The bottom line is that we as a society have to decide what it means to have a well-rounded education. In general, we all tend to agree that reading at a certain level is essential. We can argue what, exactly, that level should be, but in today’s society it’s no longer possible to function well if you can’t read and write, particularly in this increasingly Internet-driven world. Similarly, an understanding of mathematics is essential, and, from my perspective, algebra is actually a pretty low bar. True, many, if not most, people will never use much algebra, but the habits learned and the methods of using mathematics to solve problems will be useful almost no matter what a person does in life. Then, of course, there are the sciences and humanities, in particular history. If one-third of students are doing poorly at a subject that is so basic, such as algebra, then the answer is not to drop the requirement or to absolve those students who are having trouble passing it, but rather to find ways to teach it better. No one expects that everyone can excel at every topic, but there are certain topics that one should have a minimal proficiency at in order to be considered educated.
So what do you think .. Is algebra really needed in school .. and in life?
The bottom line is that we as a society have to decide what it means to have a well-rounded education. In general, we all tend to agree that reading at a certain level is essential. We can argue what, exactly, that level should be, but in today’s society it’s no longer possible to function well if you can’t read and write, particularly in this increasingly Internet-driven world. Similarly, an understanding of mathematics is essential, and, from my perspective, algebra is actually a pretty low bar. True, many, if not most, people will never use much algebra, but the habits learned and the methods of using mathematics to solve problems will be useful almost no matter what a person does in life. Then, of course, there are the sciences and humanities, in particular history. If one-third of students are doing poorly at a subject that is so basic, such as algebra, then the answer is not to drop the requirement or to absolve those students who are having trouble passing it, but rather to find ways to teach it better. No one expects that everyone can excel at every topic, but there are certain topics that one should have a minimal proficiency at in order to be considered educated.
So what do you think .. Is algebra really needed in school .. and in life?
Parent Functions
Who uses this?
Oceanographers use transformations of parent functions to approximate data sets such as wave height versus wind speed.
Oceanographers use transformations of parent functions to approximate data sets such as wave height versus wind speed.
Well, similar to the way that numbers are classified into sets based on common characteristics, functions can be classified into families or functions. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function.
" Parent Functions" : Video
As seen in this example, their are parent functions, and smaller, more specific lines and points, known as "babies" to some people. In this parent function, it shows that the line passes through zero; and the "baby" functions show where the points meet and create a linear function.
Quadratic Functions
Why Would you want to learn this?
You can use quadratic functions to model the heights of a football,baseball, or soccer ball.
You can use quadratic functions to model the heights of a football,baseball, or soccer ball.
When a soccer ball is kicked into the air, how long will the ball take to hit the ground? The height, h, in feet of the ball after t seconds can be modeled by the quadratic function h(t)= -16t²+32t. In this situation the value of the function represents the height of the soccer ball. When the ball hits the ground, the value of the function is zero.
A zero of a function is a value of the input x that makes the output f(x) equal zero. The zeros of a function are the x-intercepts.
Unlike linear functions, which have no more than one zero, quadratic functions can have two zeros. These zeros are symmetric about the axis of symmetry.
Unlike linear functions, which have no more than one zero, quadratic functions can have two zeros. These zeros are symmetric about the axis of symmetry.
" Quadratic Functions " : Video
In this example, it shows directions to graph/sketch and find the points of a parabola , and how it is used.
Polynomial Functions
Who uses this?
Doctors can use polynomials to model blood flow.
A monomial is a number or a product of numbers and variables with whole number exponents. A polynomial is a monomial or a sum or difference of monomials. Each monomial in a polynomial is a term. Because a monomial has only one term, it is the simplest type of polynomial.
Polynomials have no variables in denominators or exponents, no roots or absolute values of variables, and all variables have whole number exponents.
A monomial is a number or a product of numbers and variables with whole number exponents. A polynomial is a monomial or a sum or difference of monomials. Each monomial in a polynomial is a term. Because a monomial has only one term, it is the simplest type of polynomial.
Polynomials have no variables in denominators or exponents, no roots or absolute values of variables, and all variables have whole number exponents.
"Polynomials" : Video
Exponential Functions
Who uses this?
Collectors can use exponential functions to model the value of rare musical instruments.
Moore's law, a rule used in the computer industry, states that the number of transistors per integrated circuit (the processing power) doubles every year. Beginning in the early days of integrated circuits, the growth in capacity may be approximated by this table below:
year: 1965 1966 1967 1968 1969 1970 1971
Transistors: 60 120 240 480 960 1920 3840
Moore's law, a rule used in the computer industry, states that the number of transistors per integrated circuit (the processing power) doubles every year. Beginning in the early days of integrated circuits, the growth in capacity may be approximated by this table below:
year: 1965 1966 1967 1968 1969 1970 1971
Transistors: 60 120 240 480 960 1920 3840
Formula for an Exponential Function:
f(x)= b^n , where b > 0, b ≠ 1
f(x)= b^n , where b > 0, b ≠ 1
"Exponential Functions": Video
Rational Functions
Why learn this?
Rational Functions can be used to model the cost per person for group events, such as a band trip to a bowl game.
A Rational Function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x)= 1/x. Its graph is a hyperbola, which has to separate branches.
Rational Functions can be used to model the cost per person for group events, such as a band trip to a bowl game.
A Rational Function is a function whose rule can be written as a ratio of two polynomials. The parent rational function is f(x)= 1/x. Its graph is a hyperbola, which has to separate branches.
Like logarithmic and exponential functions, rational functions may have asymptotes. The function f(x)= 1/x has a vertical asymptote at x=0 and a horizontal asymptote at y=0.
The rational function f(x)= 1/x can be transformed by using methods similar to those used to transform other types of functions.
The rational function f(x)= 1/x can be transformed by using methods similar to those used to transform other types of functions.