prove that x^4/x^2+2 is a parabola.

Question

geerky42 · Answer

$$\dfrac{x^4}{x^2}+2$$
?

umlika · Answer

its x^4 and the numerator is x^2+2 as a whole

umlika · Answer

no i mean denomenator*

paxpolaris · Answer

$${x^4 \over x^2+2}$$

so like this ^^^ ?

umlika · Answer

yea :)

geerky42 · Answer

Well, $\dfrac{x^4}{x^2+2}$ is not polynomial function.

umlika · Answer

yeah but my teacher said that it is a parabola and we have to prove it why

paxpolaris · Answer

what is the definition of a parabola?

geerky42 · Answer

If it is not polynomial function, then it cannot be parabola.

Are you sure it's not $\dfrac{x^4}{x^2}+2$?

geerky42 · Answer

I guess definition of parabola is not really what I think it is

umlika · Answer

umm... i m preety sure that the question is what i told you, but yeah this is confusing, when i plot this on a graphing calculator it showed parabola

geerky42 · Answer

It looks like parabola, but it is not parabola, according "normal" definition of parabola.

Are you given definition? What is definition of parabola?

umlika · Answer

No, just this :/

anonymous · Answer

According to http://mathworld.wolfram.com/Parabola.html a parabola is "the set of all points in the plane equidistant from a given line and a given point F not on the line"

umlika · Answer

so this problem is not a parabola ?

paxpolaris · Answer

no i don't think so. .. it is very close to a parabola for large x. but not exactly one.