Graphing Advanced Equations

[Bob]

Hello, everyone. A couple of questions for you:

(1) Does the Nspire or Nspire CAS have the capability to graph complex
equations such as the following? If so what is the procedure for
doing so?

(x+y)^3 = x^3 + y^3



(2) What is the best procedure to find the zeros of a polynomial using
the numeric Nspire?


Thanks very much for your help.

Sincerely,

Bob

[Steve Arnold]

Hi Bob

(1) It is certainly possible to graph implicit equations of the sort you mention on both CAS and non-CAS:

* CAS: Use "zeros" after converting the equation to an expression. In this case, in Graphs & Geometry function entry line, enter

zeros((x+y)^3-x^3-y^3,y) and you will get the resulting graph (which is a straight line, y=-x - more interesting would be something like zeros((x+y)^3-x^3-y^3-1,y)!)

* non-CAS: Use "nSolve" a couple of times:

f1(x) = nSolve((x+y)^3 = x^3 + y^3,y=-2) and

f2(x) = nSolve((x+y)^3 = x^3 + y^3,y=2)

A little slow but effective.

For the zeros of a polynomial, I would suggest using the "proots" function from my polynomial toolkit - go to

http://www.compasstech.com.au/TNS_Authoring/poly.html

and download the zipped link near the top of the page (where it says TNS Poly Document under the heading)

Unzip and put at least the file "poly.tns" into MyLib.

Open a document (and Refresh Libraries) and then type in a Calculator (or spreadsheet)

poly\proots("your polynomial up to degree 4") as a string.

(This is assuming that you are using non-CAS)

If you want to do without the string, first enter

poly\pvar("x") (or whatever variable you wish to use) and then run proots.

Should give you all roots as a list.

For something a little fancier, try the related "psolve" with a quadratic: for example,

poly\psolve(2x^2-4x+5)

and it will display the source of the roots as well.

Hope this helps

Steve

With best wishes,
Steve
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Dr Stephen Arnold
Educational Technology Consultant
Compass Learning Technologies

T3 Fellow, Teachers Teaching with Technology Australia

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[Joe]

Hi Steve,
Perhaps there is more to it than "the resulting graph (which is a
straight line, y= -x." A couple of points that are not on the
diagonal line y= -x are x=1 and y=0, also y=1 and x= 0. Both of these
points satisfy (x+y)^3 = x^3 + y^3 so the x and y axis would also
seem to be part of the graph of (x+y)^3 = x^3 + y^3 because when x=0,
the equation reduces to y^3=y^3 which is true for all y, etc. Does
nspire also indicate the axes are part of the graph?
Joe

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[Steve Arnold]

You are quite right Joe - the graph is more than just y=-x and I was being a bit flippant - sorry. Visibly, though, with any graphing package, all you see for this graph is that line - the missing points and axes are not usually visible, making it a less interesting example than, say, x^3+y^3-3x*y=0, for example.

Yes, if you hover over the axes, they do show as part of the graph (although there is a little fiddling of the nsolve values to get a complete graph on the non-CAS).

Thanks for spotting that Joe

Steve

[Bob]

Thank you all very much for all of your help!. I greatly and
sincerely appreciate it!

Thanks,

Bob