Why should i learn quadratic equations

Newton also based his laws of motion on the quadratic equation by defining the acceleration of objects and forces that act upon them. He based his laws on objects falling and moving, taking into consideration the objects are on a spinning object earth , which is orbiting the our sun. Newton was not aware of the forces that act on our solar system from the rotation of the Milky Way Galaxy.

Do you think this would have mad a difference in his calculations? No the answer would still be the same; however it would have taken him longer to calculate. The quadratic equation is used by car makers to determine how much and what type of brakes are needed to stop a car going at various speeds, while it is still on the drawing boards.

This and other design functions which use the quadratic equation are part of the design steps of a new car, truck, motorcycle, and other types of automobiles. Also, who was at fault and why the vehicles were damaged the way they were. These calculations are also used by car designers to develop an even safer care for occupants during future collisions. The quadratic equation is used in the design of almost every product in stores today. I do not know how to answer as well even though I know the history behind the conjecture.

Now I am going to become a teaching assistant, I think I should be able to answer such questions before I am at the stage and someone ask me questions like "Why do I need to know calculus"?

So I post this at here. What is rather important, however, is the abstract skill of recognize a problem as an instance of a problem type for which you've heard of a canned solution, and apply the canned solution formula by plugging in parameters from the particular problem instance.

Many more people will need that than will need the specific skill of solving quadratics. The quadratic formula is a nice elementary example of a problem type that is usually easier to solve by plugging into a formula than by remembering a derivation.

It is fairly clear whether a problem is an instance of the one it solves, for example, so doesn't need a long touchy-feely discussion about whether or not it is reasonable to solve this or that problem as a quadratic equation in the first place. Such deliberations also need to be taught and learned, of course, but preferably after the mere art of plugging-into-formulas has become a trivial skill. The Universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters in which it is composed.

It is written in the language of mathematics…. Others have echoed this sentiment, but I'll add some emphasis on non-mathematical applications. Elementary algebra is really the first place where students should learn how to solve problems, rather than simply answer questions. By learning how to solve quadratics -- perhaps not through direct, rote application of the quadratic equation -- one learns how to solve problems.

By learning about the properties of polynomial equations, one learns how to solve problems. By learning about the behavior of trigonometric functions, one learns how to solve problems.

These are tools useful for math, for sure, but more importantly, they teach us to look at details, learn about the importance of essential properties, and how to formulate solutions. These are skills used in day-to-day life. The math might never be used, but the skills will be. The skill of how to approach a problem from different possible directions and formulate a solution strategy is useful in many quotidian tasks.

For instance, I recently moved. Moving has not a whole lot to do with math. But, the task of packing my things, moving them across town into a new place, and integrating those things into a slightly different lifestyle poses a problem.

Sure, I could have just put all my things into boxes, shoved it into a truck, and thrown it into the house. But probably that would have been a whole lot more work than looking at the essential properties of my belongings some are fragile, some are large, some belong upstairs, some go in the basement , and formulating a scheme that incorporates these essential properties into a comprehensive solution strategy.

And in the end, it was a lot less work than it might have been. Algebra teaches one how to evaluate a problem, formulate a strategy based on some fixed rules e.

As a topic for another forum, I feel that the problem is not so much with math education though that takes a share of the blame but with pre-algebra education: by the time students reach algebra, they've undertaken 6 or 7 years of education where all they need to do is deliver answers, not strategies. So, to the original question: why know how to solve a quadratic?

Because learning how to solve a quadratic gives you the skills to solve myriad problems from myriad domains of quotidian life by leveraging known rules and essential properties. While it may not answer your question, this is a perennial problem that reared its head recently in the New York Times.

Among lots of responses, this one is worth reading. You need to know how to do math at a decent level to perform in any science or technology job. Sure, you say calculators can solve these problems, but you need to understand quadratic equations to set up the problem in the first place. It sheds some historical perspective on the quadratic equation, including some problems that could have been the motivation for solving it - for example, how do you size a field in order to obtain a certain amount of crop production?

Also, the quadratic equation is often found in all kinds of day-to-day applications - how high do I need to aim a water jet for it to reach a certain landing spot?

How much fence do I need to buy for a triangle shaped field? Or who could forget the parabolic antenna? Answering the more general question, I think learning about history is the best way to have these kinds of answers. Almost every mathematical construct taught at college level was either devised to solve a practical problem, found applicability in various domains once it was found, or at the very least has some interesting backstory preceding or following its discovery.

All of these help give some concrete context to the abstract mathematics. Of course have in mind that being able to answer these questions will probably not solve your students' interest issues by itself! The best way to change the way we instruct is to abolish all state funded public schools, disband public unions that kick back campaign money to the supposed representatives and let the parents and local school boards freely fire the worthless drones.

Actually, the reason why we can't get good math teachers is becuase the industry hires them at a much higher rate of pay then what the schools can pay. We get the "left overs" to choose from. I lucked out, and happened to get 3 very good math teachers. But I was the exception, and clearly not the rule. This has definitely helped me understand quadratic equations.

This is a subject that I have previously struggles with an after reading this article, I can understand it much better. I enjoyed learning about the history of quadratic equations and reading the explanations. Great article and very well put out! In mathematical terms, if x is the length of the side of the field, m is the amount of crop you can grow on a square field of side length 1, and c is the amount of crop that you can grow, then".

The two are different: m is the amount you can grow on a field of unit side length and c the amount you can grow on the field under consideration side length x. So did I! I am an artist, I think graphically. Geometry, Geography, Cartography, Orthography, etc. Irrational Quadratic Equations IQE , as taught in most public schools in the United States of America, make absolutely no sense, and serve no discernible purpose in the real world.

They constantly asked on written assignments to merely, "Solve. Then they always complained about the result I wrote, even when it was correct, because they wanted me to, "Show my work. The process of going through the formula was more important to them than the result.

None of them understood that I used a different means to get to the result, that was faster, and just as accurate. I didn't understand why they insisted upon writing mathematical expressions that were needlessly complex to denote an equation that was effectively upside down, backwards, and turned inside out. For them, algebraic notation was a mathematical puzzle to be taken apart and put back together, providing 'proof' that the expression was true at all points in the progression.

I skipped the algebraic notation and went directly to the result. I didn't need 'proof', I just wanted to get the work done. I knew in my heart that no one would actually write equations of the sort they expressed when attempting to solve real world issues in an expedited manner.

This article is very well written. I wish I had come across something of this sort thirty years ago, when it could have done me some good. Instead, it wasn't until I took classes in Trigonometry that it all fell into place. Trigonometry did for me, as an artist, what Algebra did for my high school instructors. Trigonometry acted as a mathematical bridge between Arithmetic, Geometry and Algebra, that I could traverse at will.

I think it is nearly impossible that the Babylonians thought there were days in a year. I think you are implying that the number of degrees in a circle were chosen because the earth moves through almost one degree of its orbit each day. It's more likely that they chose degrees as an outgrowth of their love for the number 60 - because it has so many factors. If you choose 60 for the internal angle of an equilateral triangle you get degrees in a circle.

The radius of a circle will fit inside the circle six times exactly to form a hexagon; the corners of the hexagon each touch the circumference of the circle.

Babylonians did indeed have a love for the number 60 and if each of the sides of the hexagon are divided into 60 and a line drawn from each 60th to the centre of the circle then there are divisions in the circle. Thanks for going to the trouble of explaining the history and applications of quadratic equations. The point of it all was never explained to me when I was thrown into the deep end with them, age Now that I've been asked to explain them to a friend's son, your material is helping to demystify things.

Matt, North Wales, UK. How is this equation derived from the figure given? There's no explanation as to what "a" and "b" actually represent? I was wondering the same thing. In the diagram I take ax to be the base of the smaller triangle but then where is x in the equation coming from?

Are a and x equal? I'm also stuck on that 1st example of the field comprising 2 triangles and how we get to the quadratic equation from that. I would love to go through the rest of this article but don't want to until I've overcome the hurdle of understanding this. Please, someone? But why is the base of one triangle ax and of the other simply b. Where does that ax value come from? I can understand Anon's frustration back in Jan ' So often in mathematical explanations I've read I find myself tripping over a missing step.

Like a mathematical pothole. It's usually something so obvious to the mathematician who wrote it that it didn't seem to need mentioning. Like where that little square came from- though I did eventually work that one out. The problem is that if you are trying to follow a set of mathematical steps even if you solve the missing one as with me and the small square you have been diverted away from the main problem and lost the thread: And then probably give up and go off and do something else instead.

I'm pretty sure when they sought out ways to derive a quadratic equation to help them reason triangular regions they had to think frontwards and backwards. First, keep in mind that "m" represents a basic unit of 1. But are their heights 2x? Let's think about it, when finding the area of a right triangle we eventually divide the area by 2 after multiplying the b x the h. The larger triangular area would be b times x or bx for its area.

You asked though "what is "a" and "b"? This is my perception after being confused there for a minute too. I hope this helped you or someone just a little although it's years later- just discovered this awesome forum:. I really can't follow what you're saying. I just want to know where that expression for the height comes from. So the yield, which should be a product of area and the coefficient m is now rendered as the areas of two squares without having anything to do with that coefficient anymore.

I can see all that but I just can't grasp what on earth is going on and its doing my head in. Babylonians took over Mesopotamia at around BCE. Thanks so much I kept getting my anwsers wrong because I didn't realize you had to divide both parts by the denominato. Allaire and Robert E. I noticed a few people were confused about the choice of height for the triangle, so here is my explanation : m is the amount of crops that you can grow in 1 square unit of area.

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