What Shape Emerges from Plotting These Complex Parametric Equations?

[evo_vil]

Homework Statement

Plot the following parametric curve, defined by the following two polynomials, on the interval: $t \in (-1;1)$. What shape do you get?
$x(t) = 16243t^{14} + 520143t^{13} -798515t^{12} -185877t^{11} + 150142t^{10} + 256559t^9 -135331t^8 -170995t^7 + 594415t^6 + 558842t^5 -111145t^4 -807101t^3 + 43763t^2 + 481059t + 341$
$y(t) = -319484t^{14} -543356t^{13} + 127242t^{12} -159791t^{11} -208212t^{10} + 276926t^9 + 174816t^8 -345549t^7 -772343t^6 + 170296t^5 + 165817t^4 -343333t^3 -147652t^2 + 14574t -120$

Homework Equations

N/A

The Attempt at a Solution

Plotted both in maple and excel (couldnt get them to work in mathematica/wolfram alpha) i get a completely meaningless shape, or have i gone shape blind?

excel

maple

 

[LCKurtz]

No, you haven't gone blind. I guess I would answer the question about what shape you get by saying "I get this shape right here in this picture."

 

[evo_vil]

I guess i am going to have to go with something along those very lines...

Just thought i might be doing something wrong and should actually be getting a flower or something... but i guess not

 

[I like Serena]

Actually, your polynomials look as if they are supposed to interpolate a set of points.
So I would suspect you made a mistake with a plus or minus sign or something.

One tiny mistake will destroy the rose!

 

[evo_vil]

I do believe they are attempting to interpolate something (thats the end case of the project, to create a Lagrange interpolating polynomial for our signature) but I've copied them straight out of the pdf that has the questions in it so what you see is what I've got in front of me... ill just have to find out from the lecturer

 

[evo_vil]

ah ha...

lecturer posted the correct formulas:

$x(t) := 16243.t^{14} + 52014.3t^{13} - 79851.5t^{12} - 185877.t^{11} + 150142.t^{10} + 256559.t^9 - 135331.t^8 - 170995.t^7 + 59441.5t^6 + 55884.2t^5 - 11114.5t^4 - 8071.01t^3 + 437.63t^2 + 481.059t + 341$

$y(t) := -31948.4t^{14} - 5433.56t^{13} + 127242.t^{12} - 1597.91t^{11} - 208212.t^{10} + 27692.6t^9 + 174816.t^8 - 34554.9t^7 - 77234.3t^6 + 17029.6t^5 + 16581.7t^4 - 3433.33t^3 - 1476.52t^2 + 145.74t - 120$

does indeed interpolate a flower

 

[I like Serena]

Nice!

(Do you have a picture?)

 

[LCKurtz]

 

[I like Serena]

Nice flower LCKurtz!

 

[evo_vil]

Indeed... 'tis said flower