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November 17th, 2011, 09:01 AM  #1 
Member Joined: Aug 2011 Posts: 78 Thanks: 0  Sketch y=(x+2)^3
Hey there, To the following problem: x = 2 coordinates (2,0) y = 8 coordinates (0,8) Would you say the curve (x+2)^3 is a reflection in the xaxis of the curve y=x^2? Thanks Last edited by skipjack; November 5th, 2014 at 09:31 AM. 
November 18th, 2011, 04:03 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,624 Thanks: 2077 
No. It's the reflection in the xaxis of the curve y = (x + 2)³.
Last edited by skipjack; November 5th, 2014 at 09:31 AM. 
November 18th, 2011, 09:40 AM  #3  
Member Joined: Aug 2011 Posts: 78 Thanks: 0  Re: Quote:
Do you know of any material on it to help? Thanks again. I understand the process but the different translations I find hard to grasp. Silly as it sounds. Last edited by skipjack; December 8th, 2014 at 12:18 AM.  
November 18th, 2011, 01:29 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,624 Thanks: 2077 
Translations and reflections are easy to do for any curve y = f(x), whether cubic or not. I'll assume the positive x direction is to the right and the positive y direction is up. Just reference the list of new equations, and read the effect accomplished in comparison with the original curve y = f(x). 1. y = f(x + c) $\ \,\,$Translated left by distance c. 2. y = f(x  c) $\,\,\ $Translated right by distance c. 3. y = f(x) + c $\,\,\,$Translated up by distance c. 4. y = f(x)  c $\ \,\,$Translated down by distance c. 5. y = f(x) $\ \ \,\,\,\ \ \ $Reflected in the xaxis. 6. y = f(x) $\ \ \,\,\,\ \ \ $Reflected in the yaxis. 7. y = 2c  f(x) $\,$Reflected in the line y = c. 8. y = f(2c  x) $\,$Reflected in the line x = c. 9. x = f(y) $\ \ \ \,\,\ \ \ \ $Reflected in the line y = x. 10. x = f(y) $\ \ \,\,$Reflected in the line y = x. If you have a graphing calculator, try some of the above for the cubic graph of y = x³  3x + 2 and let us know how you get on. Last edited by skipjack; November 5th, 2014 at 09:50 AM. 
November 21st, 2011, 12:57 AM  #5 
Member Joined: Aug 2011 Posts: 78 Thanks: 0  Re: Sketch y=(x+2)^3
Thanks skipjack I appreciate the help mate 

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