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Brad Albing
Brad Albing
6/10/2013 5:01:24 PM
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Re: My answer
Derek's images aren't showing up entirely correctly, so you can see them properly by going here:

http://www.dkoonce.com/B005_Quick-plot_parabola.xls


Where you'll see his hand-calcs on one tab of the spreadsheet (as an image pasted into the spreadsheet); and, on another tab, the Excel plotted graphs.

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DEREK.KOONCE
DEREK.KOONCE
6/10/2013 4:59:34 PM
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Re: My answer
Images appear to not come through well. One can pull a spreadsheet that has them at

http://www.dkoonce.com/B005_Quick-plot_parabola.xls

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DEREK.KOONCE
DEREK.KOONCE
6/10/2013 4:48:38 PM
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My answer
It took me about 2.5 minutes to crunch the equation into a form I can plot and do the actual plot (last 30 or so seconds). My notes are below.

 Hand notes for formula manipulation

The spreadsheet (below) was used to make sure my plot matches up correctly – which when overlaid on the actual, I match pretty good (upper left). The plot on the far right was used to get the slope and help develop the coefficients into the equation I actually plotted.

spreadsheet verification

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eafpres1
eafpres1
5/31/2013 3:34:42 PM
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Completing the square, and the counts
It would appear to me that changing the form of the equation to find the slope can be done using the quadratic formula.  For some equations, this may be easy enough to do by inspection.  You note you didn't go into that part; are you suggesting there are faster methods than the quadratic formula?

Regarding the counts, I note that in the general form the slope applies to the quadratic term.  I noticed the following:

Y = m(x+c)2 + b

Y = m(Ω)2 + b

dY/dΩ = 2m

count = m, 2m+m, 2m+2m+m, 2m+2m+2m+m, ... = m, 3m, 5m, 7m, ...

m= 1: 1, 3, 5, 7,...

m=2: 2, 6, 10, 14,...

m=3: 3, 9, 15, 21,...

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RedDerek
RedDerek
5/31/2013 12:27:51 AM
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Re: Do I have this equation correct?
Do not think in the box. The equation presented is correct. This is basic math from high school and the plotting method described has several basic concepts. The final trick on quick-plotting is multiplying out to get the so-called slope of the parabola.

Plotting numerous parabolas in high school became tedious and I came up with this method on my own. There are YouTube videos that show how to set up the problem, but their final graphing method is tedious compared to my method. (I did the YouTube search after the article was written as a curiosity to see what is out on the internet.)

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DaeJ
DaeJ
5/30/2013 9:41:36 PM
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Re: Do I have this equation correct?
In my view, in the most nonlinear equation, y =  f(x), x is input and y is output. But when look this formula. Y is input and x is output. That kind expression is odd. Second, to understand for quick plot, more description may be required for this blog.

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Brad Albing
Brad Albing
5/30/2013 3:19:36 PM
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Re: Do I have this equation correct?
@Derek - good - just wanted to make sure that I hadn't taken leave of my senses.

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SunitaT0
SunitaT0
5/30/2013 2:42:25 PM
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Master
Re: Do I have this equation correct?
@Brad, I had similar doubt when i saw the equation. I read the equation as : ((54/7)y) - ((1/34)y2) .

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SunitaT0
SunitaT0
5/30/2013 2:39:59 PM
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Master
Re : Quick Plot Method for Parabolas
No graphing calculators, spreadsheets, or other tools -- just the pencil and paper, folks.

@Derek, thanks for the post. I really tried hard solving the function without using graphing calculators/spreadsheets but I couldnt. I hope you will be posting solution to this problem in future.


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RedDerek
RedDerek
5/30/2013 2:09:16 PM
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Master
Re: Do I have this equation correct?
Your first entry. Otherwise it would not be a parabola.

(54/7)y - (1/34)y2

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