Which equation is show by this graph?

Question

I've read the whole chapter on this, and I can't figure out how to figure out the equation show by this graph.

Here's a picture of the graph: http://img136.imageshack.us/img136/7967/picture1td7.png

It's multiple choice, but I'm not going to post all the choices on here because I don't want people to just pick a random one.

If you answer, please EXPLAIN your answer.

I will say that in all the answers, it's something "=4"

Meaning, to the right side of the "=" sign it just says "4", so hopefully that will give you an idea of what my teacher is looking for.

THANKS!

*TYPO*


"shown" not "show"
sorry about that.

Answer 1

This graph appears to be a very narrow parabola, but it's on its side, so it is of the form x = a * y^2.

Its vertex is on the origin and it appears to cross y=+/-1 at x=4, so I would say:

x = 4y^2

If it has to have "=4" in the solution, maybe he wants to see:

x / y^2 = 4

... though I would think that if that were the answer, the origin would be a hollow dot (it can't be part of the solution because a zero denominator is not allowed).

Answer 2

It looks to me like the graph of x = 4y^2. And I decided that before I read the bit where you said the answers all have "= 4" in them.

It's symmetrical about the x-axis, and x is always positive; furthermore, although it's not easy to tell, the ends of the graph do not seem to be levelling off to an x-value limit (though of course the value of x is changing ever more slowly). All these things combined led me to think that it was likely to be x = ky^n for some constant k and some positive even integer n.

Next, the graph appears to pass through x = 1 when y = 1/2 and through x = 4 when y = 1. In other words, doubling y leads to quadrupling x. This indicates that n = 2. (More fully, n = log 4 / log 2 which of course is 2.) Then k must be 4 to pass through the indicated points. So we conclude that the graph is probably that of x = 4y^2.

To express this as something being equal to 4 most easily gives us x/y^2 = 4, but this will not include the origin; I can't quite tell from the graph (it seems a bit blurry) whether or not the origin is included. If the origin should be included you could always express it along the lines of x - 4y^2 + 4 = 4 (or 4y^2 - x + 4 = 4, or for any nonzero k, kx - 4ky^2 + 4 = 4.) Of course, I don't know if any expression along these lines is in your answer set. ;-)