Algebra

[Amb]

If (x^2)+(y^2) = 8

How do you reorganise the equation so that y = .....

I have a whole bunch of workings that are probably wrong. I just want a formula that will calculate Y for any given X, noting that there are values of X that wont work.

[Zag]

Are you taking a class, or something?

(x^2)+(y^2) = 8 ------------------------ Add -(x^2) to both sides of the equation
(x^2)-(x^2) + (y^2) = -(x^2) + 8 ------------ [(x^2)-(x^2)] is just zero, so
y^2 = -(x^2) + 8 ----------------------------- Now take the square root of both sides. Note that y^2 and (-y)^2 equal the same thing, so we have to account for the other side being positive or negative. The symbol ± is said aloud as "plus or minus"
sqrt( y^2 ) = ± sqrt( - x^2 + 8 ) --------------- sqrt( y^2 ) is just y so

y = ± sqrt( - x^2 + 8)

If x^2 gets any larger than 8, then you'll be taking a square root of a negative number, which isn't allowed until calculus. So you might write this as

y = ± sqrt( - x^2 + 8) : [ -sqrt(8) < x < sqrt(8) ]

that is, it only has a value when x is greater than -sqrt(8) and less than sqrt(8).

If you graph this, it makes a circle with a radius of sqrt(8)

Edit: I found an online graphing tool. -- it won't let me put a URL with arguments in here, so you'll have to copy&paste

[Amb]

Actually I used to be really good at algebra back in my school days, but I havent used it since... I was mucking around making cartesian graphs in excel, and wanted a formula to graph a circle

The formula
=SQRT(POWER(-A2,2)+8) doesnt really work though, because A2=9 (aka X=9) produces 9.43

[Amb]

Oh might be =SQRT((-POWER(A10,2))+8)

[Zag]

Right. I assume that's only getting you half the circle, though.

[Amb]

Yeah but thats easy enough to overcome. Now that I see the answer, Im surprised I didnt get it earlier.

[Amb]

I read in a book that if you change the Exponent to higher numbers (even only) the graph changes from a circle to a rounded rectangle. The closer you get to infinity, the more rectangular the shape is.

Well I can tell you if you do this:

=SIN(SQRT((-POWER(A2,$D$2)) +$E$2))
(D2 = 2, E2 = 8)

You get a sponge shape



Im sure you all really care, but this is fun. Any suggestions for weird things (eg LOG) to throw into equation?

[Zag]

Can you plot four equations on top of each other? If so, plot all of these:

y= x^4 + 20 x^3 + 146 x^2 + 460x + 530
y= x^4 - 20 x^3 + 146 x^2 - 460x + 530
y= sqrt(4-x^2) +3
y= - sqrt(4-x^2) +3

Plot them for the range x from -10 to 10
and y from 0 to 6

By the way, rather than writing out POWER(X1,2), you can just write X1*X1

[Amb]

Im using POWER(x,y) because X and Y are cell references. That way I can change it to X1*X1*X1*X1 if I want.

[Zag]

Did you plot them? Can you figure out how I did that?

[MatthewV]

I feel like I am missing something. But your first equation is always going to be more than 530 when x is above zero.

And MATLAB is much nicer than Excel for this

[MatthewV]

Or maybe I just needed to read the part about x going from -10 to 10! (Fortunately I was able to change the entire plot by changing one number)

[Zag]

[MatthewV]

Hah! You didn't see post #12.

[Zag]

Not until after I'd posted, correct. So, did you graph it again?

[MatthewV]

Yes, but I didn't take a picture of it... (Hey, I said that I only had to change one number to re-graph it)

[BraveHat]

[Zag]

Yeah, yeah.