possible equation

May 2009
271
7
im supposed to find a possible equation for this graph; i know that the equation must be degree 6 cos it has five turning points but otherwise i have on idea where to start, all of my attempts on graphic calculator failed miserably.
any hints?
 

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MHF Hall of Honor
Mar 2010
2,340
821
Chicago
im supposed to find a possible equation for this graph; i know that the equation must be degree 6 cos it has five turning points but otherwise i have on idea where to start, all of my attempts on graphic calculator failed miserably.
any hints?
Fun problem, for me.

You can see six real roots. If you estimate where they are, you can write a degree six polynomial immediately (think: factoring). Then if you play around, you should be able to get it to look very much like the sketch.
 
May 2009
271
7
i tried doing that by taking x-values that seemed relatively correct graphically, but then the y-values shot through the roof...
how can this be remedied?
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
Then please show what you did. Of course, you can always control the size of y values by choosing the coefficient of the leading term correctly.
 
May 2009
271
7
i constructed something like -(x+4)(x+3)(x+1)(x-2)(x-4)(x-5)
of course that doesnt work well
how can i birng down the y-values to fit the graph?
 

undefined

MHF Hall of Honor
Mar 2010
2,340
821
Chicago
i constructed something like -(x+4)(x+3)(x+1)(x-2)(x-4)(x-5)
of course that doesnt work well
how can i birng down the y-values to fit the graph?
I graphed your function in Mathematica and took a screenshot.



I'd say you're done! :D