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Real-Life Application of a quadratic function

08/31/2007 6:33 PM

Do all real-life quadratic functions have do do with throwing something or measuring? Can someone give me an equation of a quadratic function using x and y by choosing at least two values of x to input into the function and by finding the corresponding y for each??

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#1

Re: Real-Life Application of a quadratic function

09/01/2007 6:01 AM

Nice question...

Throwing and measuring covers an awful lot of applications! So I think you pretty much have it right.

I've done a fair bit measuring stuff, and in the real world data may follow nice orderly mathematical functions for a short time (or vice versa) but then other effects kick in and it all goes haywire. I have often split data up into say 3 linear section or a couple of square functions. Most of my software is written in assembler so I try and keep it simple. There is a lot of exponential stuff about.

I guess what I'm really trying to say is that the real world doesn't fit the maths...the maths is created to try to explain, fit, model, calculate, predict the real world.

If all else fails use a look up table!

Dunno if this is of any help at all!

Del

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#11
In reply to #1

Re: Real-Life Application of a quadratic function

09/04/2007 8:28 AM

Dang! Are you still using Assembly language programming? For PDP-8 by any chance? I miss those days . . .

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#15
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Re: Real-Life Application of a quadratic function

09/04/2007 4:36 PM

Yup..I remember them...

I'm programing microcontrollers...mostly assembler, some C.

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#2

Re: Real-Life Application of a quadratic function

09/01/2007 10:08 AM

I thought it would be easy to fill a page but I seem to have a HD affected memory.

Parabolic mirror, water channel, sound reflector.

The outlet of a nozzle.

The shape of a spillway for a dam.

Light and signal intensity.

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#3

Re: Real-Life Application of a quadratic function

09/02/2007 6:35 AM

Quadratic equations are used considerably in computer networking. They're used for all sorts of error checking, as well as encryption. Is this the sort of thing you're looking for? They're also used in the mathematics of Quality of Service (Qos), the concepts of understanding how to dynamically allocate and share bandwidth.

On the other hand, if you're a general contractor, and a customer wants a weirdly shaped concrete patio, for instance, being able to fit that shape into a quadratic equation makes it a lot easier, using calculus, to determine it's area and volume.

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#4

Re: Real-Life Application of a quadratic function

09/02/2007 8:31 AM

No, but...

I was going to suggest that the learning curve is an example, but then I confirmed its actually exponential...

http://www.directives.doe.gov/pdfs/doe/doetext/neword/430/g4301-1chp21.pdf

The fact that the exponent is ^2 while the inputs are ^1 indicates that it would solve perimeter vs area (fencing) problems, or bill of materials issues for tanks and containment etc. see last example below.

Actually it is used a lot in optimization problems where you need to find minima or maxima.There is a great application regarding AIDS here: http://www.math.lsa.umich.edu/courses/105/Handouts/m105_f05_h4.pdf

how about this:

A rancher has 600 meters of fence to enclose a rectangular corral with another fence dividing it in the middle as in the diagram below.

As indicated in the diagram, the four horizontal sections of fence will each be x meters long and the three vertical sections will each be y meters long.

The rancher's goal is to use all of the fence and enclose the largest possible area.

The two rectangles each have area xy, so we have

total area: A = 2xy.

There is not much we can do with the quantity A while it is expressed as a product of two variables. However, the fact that we have only 1200 meters of fence available leads to an equation that x and y must satisfy.

3y + 4x = 1200.

3y = 1200 - 4x.

y = 400 - 4x/3.

We now have y expressed as a function of x, and we can substitute this expression for y in the formula for total area A.

A = 2xy = 2x (400 -4x/3).

We need to find the value of x that makes A as large as possible. A is a quadratic function of x, and the graph opens downward, so the highest point on the graph of A is the vertex. Since A is factored, the easiest way to find the vertex is to find the x-intercepts and average.

2x (400 -4x/3) = 0.

2x = 0 or 400 -4x/3 = 0.

x = 0 or 400 = 4x/3.

x = 0 or 1200 = 4x.

x = 0 or 300 = x.

Therefore, the line of symmetry of the graph of A is x = 150, the average of 0 and 300.

Now that we know the value of x corresponding to the largest area, we can find the value of y by going back to the equation relating x and y.

y = 400 - 4x/3 = 400 -4(150)/3 = 200.

Does this help?

Source: http://dl.uncw.edu/digilib/mathematics/algebra/mat111hb/P&r/quadratic/quadratic.html

milo

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#7
In reply to #4

Re: Real-Life Application of a quadratic function

09/03/2007 3:26 AM

Yes! That's an oldie, but a goodie!

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#5

Re: Real-Life Application of a quadratic function

09/03/2007 3:13 AM

I'm working on a formula that can predict my wifes mood, but it seams that quadratic is not sufficient.

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#6
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Re: Real-Life Application of a quadratic function

09/03/2007 3:25 AM

Even harder... Predicting your ex-wife's mood.

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#16
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Re: Real-Life Application of a quadratic function

10/21/2012 1:05 PM

Predicting the wife's mood is far more difficult than predicting the ex's mood and is well beyond the scope of this post as well as being well beyond the sum total Mathematics known to Man..er..Men, but probably most closely related to Catastrophe Theory but whose fundamental operators resemble bifurcation fractals - the same fractals which 'predict' variations in locust populations. You know how it goes - you're just jaunting along, spending a nice afternoon with your wife, somebody leaves a spoon out on the counter and, before you know it, the world's crops are decimated, leaving you none the wiser and a wee bit hungry. Like the Butterfly Effect, except that you don't have to wait six months. More like six femtoseconds. On a Good Day.

The ex's mood is much simpler to model and is nearly always a function of the form y = (L!*i)^666 where y maps to You, L is a constant representing the extent to which you *imagined* she Liked you before she became an ex, whilst i is of course the imaginary constant i = sqrt(-1). The result is always Real, as you know.

:)

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#10
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Re: Real-Life Application of a quadratic function

09/04/2007 8:26 AM

Have you tried the complex plane using imaginary numbers?

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#12
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Re: Real-Life Application of a quadratic function

09/04/2007 8:52 AM

Yes, it resulted in some nice chaped planes and curves, which turned her mood to the wrong side again.

There must be an extra dimension in the number field, perpendicular to the imaginary and real axis. I'm sure that this will enable man to understand women.

Bur, we are just not ready for it, otherwise they would have explained us.

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#13
In reply to #12

Re: Real-Life Application of a quadratic function

09/04/2007 9:15 AM

Hmmm . . . Would that third orthogonal plane be called the "mystery" plane?

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#14
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Re: Real-Life Application of a quadratic function

09/04/2007 9:18 AM

Who knows what happens when you square a mystery number.

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#8

Re: Real-Life Application of a quadratic function

09/03/2007 7:48 AM

For sake of brevity, out of many, a typical application for quadratic equations is a vehicle's suspension.

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#9

Re: Real-Life Application of a quadratic function

09/03/2007 12:51 PM

Want to consider throwing something mathematically? You got one!

Throwing something in real world is governed by two physics measures that is horizontal velocity and vertical velocity. Each has different characteristic, that is horizontal velocity ideally being constant and vertical velocity being perturbed by gravity acceleration.

The word 'ideally' refer to condition that the air friction and air drag is considered nil and the maximum height not too large as gravity acceleration decrease with the height.

In horizontal motion we have x the distance traveled in time t as:

x = V0x . t ; V0x is horizontal initial velocity

Rearranged for the time we have t = x / V0x (we use this soon)

In vertical motion we have y the height traveled in time t as:

y = V0y . t - 1/2 g t2 ; g is gravity acceleration

substitute the time t:

y = V0y . (x / V0x) - 1/2 g (x / V0x)2

rearrange to have nicer look:

y = (V0y / V0x). x - x2 / 2g(V0x)2

Now we have the height y traveled as a function of x, and in quadratic form as required :)

V0y and V0x often be derived from one initial velocity V0 with elevation angle from horizontal α.

V0x = V0 . cos α ; V0y = V0 . sin α

This new view leading to new sophisticated and more practical from :

From: y = (V0y / V0x). x - x2 / 2g(V0x)2

To: y = a.x2 + b.x + c

with :

a = - 1 / (2g V02 . cos2 α)

b = tan α (recall that tan α = sin α / cos α)

c = initial height if you throwing from above ground level.


From the last equation, you will easily derive the highest achievement, the maximum target distance on the ground and time to hit the target. They are on your side :)

Have a happy throwing !

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