Author Topic: quadratic equations (white flag goes up)  (Read 11866 times)

Martin

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quadratic equations (white flag goes up)
« on: September 15, 2009, 10:04:49 pm »
I've just spent many hours failing to find a solution either online or via MyMaths to my 13yo's maths homework, as someone who managed a grade A GCE  30 years ago, has maths changed that much?

WTF are Original Sequences; First and Second differences?   >:(

more importantly; what possible bloody use is any of this in the National Curriculum other than to keep maths teachers off the streets?

Re: quadratic equations (white flag goes up)
« Reply #1 on: September 15, 2009, 10:10:47 pm »
WRT to your last question: I don't know; never heard of this terminology in the context of quadratic equations. I must be getting old, or becoming to specialised in solutions of PDEs!

What was your son's mathematical problem?
Frenchie - Train à Grande Vitesse

Re: quadratic equations (white flag goes up)
« Reply #2 on: September 15, 2009, 10:11:19 pm »
Dunno - we never used those terms.

Has anyone ever used a quadratic equation in Real Life (TM)?  ISTR they tell you where a quadratic curve cuts the axes, which must be really useful when the final breakdown of society comes and you've lost both the matches and the tin opener.
Never tell me the odds.

Martin

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Re: quadratic equations (white flag goes up)
« Reply #3 on: September 15, 2009, 10:13:16 pm »

What was your son's mathematical problem?

"write down an nth term formula for the original sequence
12 26 46 72 104 142"  ???

a Freddered gold 1 point star to the first (non maths teacher) who can come up with the correct answer  :thumbsup:

Re: quadratic equations (white flag goes up)
« Reply #4 on: September 15, 2009, 10:17:56 pm »
I use quadratic polynomials to reconstruct numerical solutions; e.g. in the case of a thin film model in fluid mechanics (imagine an oil film) I know the velocity at the wall, the mid-depth velocity from a depth average solution and the shear at the film surface from which I must reconstruct a velocity profile to obtain the velocity at the surface. In this case a cubic interpolation would be better but more difficult to implement. This is just one example of a mathematical solution to an engineering problem I work on right now (for an aeroengine application, so very practical  :)).
Frenchie - Train à Grande Vitesse

Martin

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Re: quadratic equations (white flag goes up)
« Reply #5 on: September 15, 2009, 10:19:50 pm »
I don't think designing aero engines features in year 9  :-\

Re: quadratic equations (white flag goes up)
« Reply #6 on: September 15, 2009, 10:20:23 pm »
I don't think designing aero engines features in year 9  :-\

I'm not a designer...  ;)
Frenchie - Train à Grande Vitesse

Re: quadratic equations (white flag goes up)
« Reply #7 on: September 15, 2009, 10:26:07 pm »

What was your son's mathematical problem?

"write down an nth term formula for the original sequence
12 26 46 72 104 142"  ???

Gee, I'm not even sure that I understand the question. [I did study mathematics, I promise]
Frenchie - Train à Grande Vitesse

Re: quadratic equations (white flag goes up)
« Reply #8 on: September 15, 2009, 10:27:55 pm »
3n^2 - 7n + 6 ...?
Destroying rainforest for economic gain is like burning a Renaissance painting to cook a meal.  EOW.

Re: quadratic equations (white flag goes up)
« Reply #9 on: September 15, 2009, 10:31:03 pm »
The first differences are the differences between the numbers, so 14, 20, 26, 32 etc. The second differences are the differences between these, which is a constant 6.

So from this you should be able to write a formula for the nth term, but I can't at this time of night ???

Martin

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Re: quadratic equations (white flag goes up)
« Reply #10 on: September 15, 2009, 10:31:28 pm »

Wowbagger

  • Dez's butler
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Re: quadratic equations (white flag goes up)
« Reply #11 on: September 15, 2009, 10:32:29 pm »
I noticed that the differences between the consecutive numbers increased by 6 each time. Can I have a C please?
Oh, Bach without any doubt. Bach every time for me.

border-rider

Re: quadratic equations (white flag goes up)
« Reply #12 on: September 15, 2009, 10:32:39 pm »
12 + 11n  + 3n2

I think

clarion

  • Tyke
Re: quadratic equations (white flag goes up)
« Reply #13 on: September 15, 2009, 10:33:47 pm »
3n^2 - 7n + 6 ...?

nope

No, I've been running that one through in my head, and it doesn't fit, but I can't remember how to derive the function.

Anyway, we're not really talking quadratics; this is Series work.
Getting there...

clarion

  • Tyke
Re: quadratic equations (white flag goes up)
« Reply #14 on: September 15, 2009, 10:34:57 pm »
12 + 11n  + 3n2

I think

Not that either, but it's close.  Should there be a minus sign?

*too late at night*
Getting there...

Martin

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Re: quadratic equations (white flag goes up)
« Reply #15 on: September 15, 2009, 10:35:06 pm »
12 + 11n  + 3n2

I think

how can 12+11n+ 3n[sp]2=12? (unless n=0)

border-rider

Re: quadratic equations (white flag goes up)
« Reply #16 on: September 15, 2009, 10:35:39 pm »
12 + 11n  + 3n2

I think

Not that either, but it's close.  Should there be a minus sign?

*too late at night*

It works if you start at n=0

Re: quadratic equations (white flag goes up)
« Reply #17 on: September 15, 2009, 10:36:00 pm »
12 + 11n  + 3n2

I think

And n is the rank of each number in the sequence, n = [1 ... n]? Doesn't seem to work.

How is this quadratic function or polynomials math?

[Edit: Beaten by Clarion]
Frenchie - Train à Grande Vitesse

border-rider

Re: quadratic equations (white flag goes up)
« Reply #18 on: September 15, 2009, 10:37:21 pm »

How is this quadratic function or polynomials math?

[Edit: Beaten by Clarion]


Cos a quadratic is just an eqn with x2 in, innit ;)

Re: quadratic equations (white flag goes up)
« Reply #19 on: September 15, 2009, 10:38:03 pm »

How is this quadratic function or polynomials math?

[Edit: Beaten by Clarion]


Cos a quadratic is just an eqn with x2 in, innit ;)

Just a shape function in this case... <shrug shoulders>
Frenchie - Train à Grande Vitesse

border-rider

Re: quadratic equations (white flag goes up)
« Reply #20 on: September 15, 2009, 10:39:41 pm »
Doesn't seem to work.


It does.

slightly edited:

y= 12 + 11x  + 3x2 is the equation of a quadratic curve, and if you insert the discrete points n = 0, 1, 2 etc you get the series that Martin gave us.



Re: quadratic equations (white flag goes up)
« Reply #21 on: September 15, 2009, 10:40:56 pm »
Doesn't seem to work.


It does.

It's the equation of a quadratic curve, and if you insert the discrete points n = 0, 1, 2 etc you get the series that Martin gave us.


Aha! I started at n = 1...

[Edit: at least I'll be ready for Baby G when she reaches that age!  ::-)]
Frenchie - Train à Grande Vitesse

Martin

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Re: quadratic equations (white flag goes up)
« Reply #22 on: September 15, 2009, 10:41:57 pm »
the problem I have with all this is that it it just maths for maths sake; nobody is ever ever going to need this apart from maths teachers

my work involves similar levels of anality but it does at least relate to something that exists in the real world and may one day affect people which this doesn't.

border-rider

Re: quadratic equations (white flag goes up)
« Reply #23 on: September 15, 2009, 10:43:37 pm »
the problem I have with all this is that it it just maths for maths sake; nobody is ever ever going to need this apart from maths teachers

or anyone who does a Physics degree or a PhD....

Academic subjects are always like that though, eh ?

Re: quadratic equations (white flag goes up)
« Reply #24 on: September 15, 2009, 10:44:31 pm »
Yes, but, mathematics is a toolbox or a vehicle to help one formulate solutions to science and engineering problems. When I work with people who can't express themselves or read it, it is, in my field, quite difficult to be creative.
Frenchie - Train à Grande Vitesse