definition of quadratics

Quadratic functions are functions of the second degree. It means, the highest exponent of the function is always 2. The standard form of quadratic function is f(x) = ax²+bx+c, where x represents a variable. a, b, c are  constants with a condition that a ≠ 0, otherwise the function will become a linear function. The constants a, b, and c respectively are called the numerical coefficients of the function.  ax² to be the quadratic term, bx as the linear term and c to be the constant term.

The term quadratic comes from the Latin word “quadratus” which is the Latin word for “square”. (Read more…)

History of Quadratic Functions

The development or derivation of a mathematical idea is usually as logical, deducible and rectilinear as possible. It brings about the common notion that its historical development is similarly as continuous, logical,  and rectilinear: one mathematician picking up an idea where one mathematician left it.

Using quadratic formula for example, it will be shown that the historical development of… (Click)

Educational Videos on Quadratic Functions

Ways to solve Roots of Quadratic Functions

There are four ways in solving for the roots of quadratic functions. It doesn’t matter what method you will use because you will still be getting the same result. It’s just very important that you should familiar yourself with the steps or formulas in solving for the roots. (click the following links.)

1. Graphing Quadratic Functions

2. Factoring Quadratic Functions

3. Quadratic Formula

4. Completing the Square

After learning the different methods in solving for the roots of quadratic functions, be ready for the applications of the function and some exercises. (Go next)

Applications of Quadratic Function

Quadratic function is very much important in many other field not only in mathematics. There are a lot of applications of quadratic equations whether it be in science, engineering, art, economics, athletics and to real life situations. (Click here)

Sample problems on the application of quadratic functions can also be learned in a way that we could apply it in our own simple real life situations. (Click here)

In solving word problems involving application of quadratic function, it is very important that we must familiarize ourselves with the necesssary steps in order to come up with the correct equation for the solution. There is a General Strategy for Solving Verbal Problems, with examples to follow as practice exercises.

Any question about the applications of quadratic function? Quite difficult? Oh common, try again if you want. Otherwise, try the exercises… (GO)

Exercises

The following are exercises which could enhance our abilities in solving for roots of quadratic functions.

A quadratic function is a function whose equation is a second degree polynomial. Thus, if f is a quadratic function, then f ( x ) = a x² + b x + c for constants a, b, and c, with a not equal to zero.

1.Why will a not equal zero for quadratic functions?

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The graph of a quadratic function is a parabola. The parabola opens upwards if a > 0 and opens downward if a < 0. The graph is symmetric about the vertical line x = – b / ( 2a ). The vertex of the graph has x coordinate – b / ( 2a ).

2. Find the range of the quadratic function. f ( x ) = 2 x² + 8 x + 1

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The zeros of a function are the input values which result in an output value of zero.

3. What formula did you learn in algebra which allows you to find the zeros of a quadratic function?

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4. Find the zeros of the quadratic function in #2.

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Theres another way to find the zeros of a quadratic function when the quadratic expression can be factored. For example, let f ( x ) = x² – x – 6 = ( x - 3 ) ( x + 2 ). Then, clearly, the zeros are 3 and – 2, since those are the input values which will result in an output value of zero.

5. Find the zeros of f ( x ) = – x² + 4 x + 5

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6. Sketch the graph of the function in #5. Specify the coordinates of the vertex and the x and y intercepts.

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There is an alternate way to write the equation of a quadratic function using the technique of completing the square which you learned in algebra. For example, let f ( x ) = – x² + 4 x + 5. First, subtract the 5 from both sides, then divide both sides by the coefficient of x² to get

[ f ( x ) - 5 ] / ( – 1 ) = x² – 4 x. Next, add the square of half the coefficient of x to each side of the equation to get [ f ( x ) - 5 ] / ( – 1 ) + 4 = x² – 4 x + 4. The expression on the right is now a perfect square–the square of ( x – 2 ). [ f ( x ) - 5 ] / ( – 1 ) + 4 = ( x – 2 )². Next, subtract the 4 from each side and multiply both sides by – 1 to get f ( x ) – 5 = – ( x – 2 )² + 4. Finally, add 5 to both sides to get f ( x ) = – ( x – 2 )² + 9. The advantage of this form of the function is that we can now see that the graph of f is just the graph of y = – x² shifted 2 units to the right and 9 units upwards. We can also see that the vertex of the graph is at the point (2,9). The process of completing the square can be used to re-write a quadratic function in the form f ( x ) = a ( x – h )² + k where ( h,k ) is the vertex and the graph is just the graph of y = a x² shifted h units horizontally and k units vertically.

7.Complete the square on the function and sketch the graph: f ( x ) = 2 x² – 4 x + 3

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Assessment about Camp Blog…

How is my camp blog experience so far?

Camp Blog is honestly the best camp I’ve ever attended in my whole years of teaching. Aside from the fact that it’s my first time to see the place of Pampanga, Camp Blog is actually my first national seminar. (Take note: first national seminar and a good ladder for promotion, hehe). The camp gave me opportunities to explore the very wide-range of computer world! I’m doing great, really! I can’t  imagine myself doing my own blog site. My site might not be the best but of course I’m still proud of it since I made it myself.

What do I like best?

What I like best about camp blog is the objective itself- to train us in creating our own blog site in order that we will eventually learn and apply it to our teaching-learning process.  I also appreciate the Team Managers for being accomodating and considerate. I like the venue (except the aircon)  as well.

What do I like least?

Its the pressure in finishing all assigned tasks. I really hate the air-conditioned rooms during lectures. It made me sick.

What wordpress feature am I most interested to use?

Though it’s really my first time to encounter wordpress, there’s a lot of features i really wanted to use. WordPress being open source of blog is really usefull in publishing articles whether it be for personal info or for creating ideas which we could share to others. What’s really interesting for wordpress is its ability to edit information even if it is already published in the site.  We can also insert or upload images or videos with just a click of a second or two. WordPress also has features like widgets as well as themes which can be installed easily. Through wordpress, we can also link our personal accounts in facebook or friendster and even customize our own site.

test post

Mathematical tools can be algorithms, solving equations, creative/productive tools etc, and they all go into the learning of maths. Teachers are even more key in the case of mathematics. Which tools do we need to know in mathematics, what is necessary non-digital tools? Sketch and plot using graph paper is. But finding a square root is not. This is continuously changing, and we need to discuss this all the time. The same goes for symbols and material objects like rulers. Spreadsheets represent a versatile tool that could be used in several exciting ways. read more…

 

According to a 2002 survey on the use of ICT in 100 Philippine public secondary schools, in the majority of high schools less than half of their teachers and students are able to use the computer as an educational tool.

Why did I choose my topic?

I like math, I always will. Not because I’m a math teacher but for the fact that I see a very strong demand in the fields of mathematics. In reality, math plays a very important role in our lives. From the time we wake up, to the hour that we go to bed, we cannot underestimate the importance of mathematics. We cannot deny the fact though that millions of students really hate the subject.

As an educator, its my responsibility to encourage my students to at least appreciate the beauty of math. I wanted to share my knowledge and ideas to my students. I wanted to remove the doubt of many that math is a difficult subject. Sometimes its so discouraging to note that achievement test results in math is always the lowest. That’s actually the challenge. Though there has been many opportunities abroad, the challenge reminds me that I must not fail my students. I must give them worthy ideas that they deserve so that in the near future they will also be someone who will eventually like math.

I choose Quadratic function to be my specific topic in math because I’ve discovered a new way in solving for the roots of quadratic equations. Through my blog, I hope everybody would enjoy and learn the concept well.

tenks much!

The Exciting World of Camp Blog 1B!

New place… New faces… New knowledge and ideas!

My experience in this camp blog is really extraordinary. I was so excited to meet people from different places. At first I thought I would not able to meet new friends because people find me really “suplada”, but in reality im not.  My first day here was quite good;  I met mam Josie and Hanna, co-participants from Tarlac. The following days was really so exciting! We we’re grouped according to our interest. Mam Virma Pangilinan who happened to be our Team Manager is very much happy with our group. My groupmates are equally active in participating to all activities. Sir Zaldy- the Pooh-look-a-like;  Sir Bonie-the father of the group; Sir Ramie-the unofficial photographer of the group; Sis Roland-the very serious type;  Noel, Dereck, Cyrill, Jamaica, Fely and Mara- all sweet of them are my groupmates. In fact, our group has the least number of members but we we’re tagged to be “THE MOST TALKATIVE”! (Yeah, right!)

Camp Blog 1B is  so far the best camp I’ve ever attended. We are housed in classy villas, we always enjoy sumptuous meals, we have very accomodating Team Managers, dynamic resource speakers, and of course an air-conditioned rooms during sessions that caused me cough. (Honestly I am not used in a room like this. I don’t even use electric fan, LoL!).

 

Time’s running so fast guys! We have to remember that we are here for a purpose. When we go back to our stations, let’s not forget mam Alex, mam Leila and sir Cp that without them, we might not be here, right? KUDOS to the three of you! KUDOS to CICT! Hope to see you all again for the next camp. (Favor please! Include me again for the next, hehe…)