How do I isolate the x in y = 4x - x^2?

Question

hartnn · Answer

why do you need to isolate x from there ?

anonymous · Answer

I need to express the function in terms of y

istim · Answer

Maybe it's just really late....but isn't that already "y"?

anonymous · Answer

...ok i meant in terms of x then whoops

istim · Answer

Oh. Ha ha. Made me confused.

anonymous · Answer

basically i need to turn it into a "x=" form instead of "y="

istim · Answer

Herrhhh....What grade/course level is this?

anonymous · Answer

I actually need this for a calculus proble, but I'm having a brain fart.

istim · Answer

OH..so ln and e^x and all that?

anonymous · Answer

i need to find the radii of the "outer circle" and "inner circle" of the cross section that looks like a donut, so in order to express the radius in terms of the equation, i need it in terms of "x="

istim · Answer

Or do you have to do derivatives too?

anonymous · Answer

I'm using integrals because I need to find the volume of a graph rotated around the y axis

anonymous · Answer

why dont you just complete a square

istim · Answer

Wait..does that diagram incldue x,y, z planes, or is that just 2D?

anonymous · Answer

It should be 3D. Okay, the reason why I'm asking this "x isolation" question is because I need to find the volume of the graph of y = 4x - x^2 rotated around the y-axis and bounded by y=0.

hartnn · Answer

completing the square will do it., do you know how to ?

anonymous · Answer

That's the whole problem I'm working on right now.

anonymous · Answer

I tried using the quadrative formula, but I got a numerical answer. Am I using it wrong? I'm having a big brain fart right now T_T

anonymous · Answer

if you ever need to solve a quadratic just complete a square

anonymous · Answer

in this case you need to solve for x, so complete a square to do it o_o

anonymous · Answer

I'm not trying to solve it though. I need to have the x isolated :( Solvng it gives me a numerical answer.

anonymous · Answer

-I feel really stupid right now lol-

istim · Answer

Hey, don't say that, or I'll feel stupid for not remembering anything.

hartnn · Answer

let me give you first few steps....
y= 4x-x^2 = -(x^2-4x+4-4)
 -y = (x-2)^2-4
now can you isolate 'x' ?

anonymous · Answer

they condition us to grow accustomed to f(x)!  f(y) is just as important =[

anonymous · Answer

GOD BLESS YOU HARTNN lol

anonymous · Answer

Thank you everyone, I've got it now :) haha

hartnn · Answer

lol! you too :)

hartnn · Answer

welcome ^_^