Is it possible for a parabola to not touch any axis?

[NissanSkylineN1]

So today in Math class, I wondered if there is such a function where a parabola can't touch any axis. The night before, I had discovered the function Y=1/X , where the parabola forms an L shape.

So, I went home, and asked my dad if its possible (He has a PHD in Civil Eng.). He said it must be, but then my brother interjected and said the same thing that my teacher said. One of the lines WILL touch an axis no matter what.

So, we all came to a conclusion that a parabola rotated at a 45 degree angle, opening away from the origin in the top right quadrant of a graph will do it. After a lot of trigonometry and linear calculations (Most I didn't understand a thing, since it was beyond grade 10 math), we came to a conclusion and an equation:
f(X)=X^2+y^2-√2 x-√2 y-2xy+2√2

..So, is it possible? I plotted it in MS Word and it gave me two lines, both not touching the axis, but in L shapes.....

 

[Team THRT Drift]

Wait, 1/X is not a parabola. That's an asymptote, and asymptotes never touch the axises... a parabola is X^2

Edit..

Whoops sorry, wrong word, you're right. Yes a parabola never touches the axises, it goes to negative and positive infinity. Type these in your calculator; 1/X (generic function) , 1/X^2+1, 1/X^2-1. You'll see that it doesn't touch.. no matter how you rotate it, it won't it's like an asymptote

 

[NissanSkylineN1]

Woops, you're right. I keep calling things parabolas.... awkward.

 

[Keef]

Terminology mix-ups aside, what is the question exactly? I gather that you're wondering...

Parabolas can occur anywhere in space so of course it's possible for them to never cross the x- or y-axis.

For example, if a parabola in Q1 which opens up had a vertex y>0 and X=0 was an asymptote, the parabola would never touch either axis. The sides of a parabola are not infinitely wide and will eventually approach asymptotes which they will never touch.

 

[Omnis]

If the axes are asymptotes, yes.

 

[NissanSkylineN1]

So I graphed the equation in excel... and it works! The equation I posed above is the sum of x1=x0+x1COS(alpha)+ySIN(alpha) and y1=y0-x1SIN(alpha)+yCOS(alpha).

 

[Skython]

Oh please no! These things make no sense! I remember saying, "This is so difficult, it's like Algebra." And then I realized the reason why it was LIKE Algebra.

 

[Simple Matt]

Oh please no! These things make no sense! I remember saying, "This is so difficult, it's like Algebra." And then I realized the reason why it was LIKE Algebra.

Hahaha this is why I dropped out of Math C I hated this sort of stuff.. And imaginary numbers /cringe

 

[Bopop4]

Or you could just make it y=10(x-1000)+1 (Put in little square sign.)

It would never cross the x or y.

 

[Anathema]

Gah, math.

I'm good at it, but I don't necessarily LIKE it.

 

[Bopop4]

Lol, ignore my last post.
I was thinking of aestubluesthu.......s, with the exponential functions.

 

[Keef]

So I graphed the equation in excel... and it works! The equation I posed above is the sum of x1=x0+x1COS(alpha)+ySIN(alpha) and y1=y0-x1SIN(alpha)+yCOS(alpha).

What's with all the fancy trig and crazy stuff? All you need is one quadratic divided by another quadratic to get your "L-shaped" things. Don't feel like doing math right now but if the x- and y-axis are asymptotes in that situation then the graph will never touch them.

You've made an equation that is only half a graph and has two slant asymptotes from the looks of it. I think that's a bit deep for 10th grade math over here.