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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

**Find all values of p such that 2(x+4)(x-2p) has a minimum value of -18**

This problem appears in another thread and is answered algebraically there. We will do it using geogebra.

1) Create a slider on the screen and call it p and range it from -20 to 20.

2) Enter in the input bar 2(x+4)(x-2p) and the f(x) = 2(x+4)(x-2 *1) will be created. Zoom the screen to see the parabola you have just made.

3) Enter in the input bar Min(f(x), -20, 20) and the point A will be created at the minima of the parabola.

4) Notice that the default values find the first p that is a minimum with a value of -18. Told you book problems are easy.

5) Move slider with the arrow keys and find the other value for p.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,847

Well, that works very well!

But I'm sorry, I don't know how it works. Could you explain it to me? I don't understand parabolas (although I think I came across them in high school), nor what f(x) is/does, or how it helped create the parabola.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Sorry for the delay but I am attending a meeting and will be tied up all day.

f(x) is fancy math notation for the statement y = f(x) which is read y is a function of x, meaning y depends on x.

Are you familiar with functions in programming? You can think of it here as x being the argument for the expression f(x) = 2(x+4)(x-2p).

I should not have used the term parabola. Here we are graphing a quadratic equation y = a x^2 + b * x + c. Just expand out 2(x+4)(x-2p) to see that.

f(x) = 2(x+4)(x-2p) is what geogebra used to make the curve you see on your screen.

For much more about parabolas go here:

http://www.mathsisfun.com/geometry/parabola.html

How can I help further?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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How do you know that p is within -20 to 20? What happens if there is a value of p but we carelessly slide past it?

*Last edited by Agnishom (2014-04-07 05:32:07)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

You can demonstrate that with geogebra sort of but it is easier using M.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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With M? How?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Solving:

Notice they are both the same so we have:

Solving this for p we get:

Substituting in 1)

The proof that there is only 2 p's should be apparent to you.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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What about my M code?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Hmmm, you can not translate to M?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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My post does not make sense because you've edited the post above it. Do you remember my M code?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

I am not following you, I have edited no post recently. I do not remember your code line by line.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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You've edited post 7 ofcourse.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

You've edited post 7 ofcourse.

I made some changes in the latex as I was doing it yes. I also deleted the line saying I was going to post the answer there. Why should I leave that?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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I am not saying that you have done something wrong. I am just stating that post 8 does not make sense because post 7 was changed.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,262

Post #7 answers post #6. I see what you are saying.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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