Find the polynomial

[moronatmath]

Can I please get some help on this problem? Thanks!

The curve above is the graph of a degree 4 polynomial. It goes through the point (5, -210). Find the polynomial.

f(x) =

 

[tkhunny]

What have you tried?

Off the top of my head, it looks like y = x^2 * (x^2 - 4) would be a good place to start looking.

 

[stapel]

Imageshack seems to be having some problems; it doesn't appear to be serving up the image at the moment.

Please reply with a description of the graph, including the coordinates of all marked points (such as zeroes) and the behavior (increasing, etc) over the various intervals of interest.

Thank you.

Eliz.

 

[moronatmath]

The graph looks exactly like a mcdonalds arch. I think I just did a typo in the code. It should work now.

 

[tkhunny]

Great. Now that we've cleared that up...

What have you tried?

 

[pka]

With a double root at x=0 the equation is y=Kx<SUP>2</SUP>(x−2)(x+2)
When x=5, y=−210. So use that to find K.

 

[moronatmath]

i get -.4 when I plug all of that in...which is still wrong

 

[soroban]

Hello, moronatmath!

i get -.4 when I plug all of that in...which is still wrong

Who says it's wrong?

If this is an online problem, "they" may accept only one form of the answer.

Your answer: \(\displaystyle \,y\:=\;-0.4x^2(x^2\,-\,4)\) is correct.

Have you tried: \(\displaystyle \,y\:=\:0.4x^2(4\,-\,x^2)\,\) or \(\displaystyle \,y\:=\:\frac{2}{5}x^2(4\,-\,x^2)\,\) or \(\displaystyle \,y\:=\:1.6x^2\,-\,0.4x^4\)