## ctmusicgirl7 2 years ago How do I isolate the x in y = 4x - x^2?

1. hartnn

why do you need to isolate x from there ?

2. ctmusicgirl7

I need to express the function in terms of y

3. IsTim

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

4. ctmusicgirl7

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

5. IsTim

Oh. Ha ha. Made me confused.

6. ctmusicgirl7

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

7. IsTim

8. ctmusicgirl7

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

9. IsTim

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

10. ctmusicgirl7

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="

11. IsTim

Or do you have to do derivatives too?

12. ctmusicgirl7

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

13. binarymimic

why dont you just complete a square

14. IsTim

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

15. ctmusicgirl7

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.

16. hartnn

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

17. ctmusicgirl7

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

18. ctmusicgirl7

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

19. binarymimic

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

20. binarymimic

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

21. ctmusicgirl7

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

22. ctmusicgirl7

-I feel really stupid right now lol-

23. IsTim

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

24. hartnn

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' ?

25. binarymimic

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

26. ctmusicgirl7

GOD BLESS YOU HARTNN lol

27. ctmusicgirl7

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

28. hartnn

lol! you too :)

29. hartnn

welcome ^_^