My Math Forum Sketch y=-(x+2)^3

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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 x-axis 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: 20,370 Thanks: 2007 No. It's the reflection in the x-axis 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
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 Originally Posted by skipjack No. It's the reflection in the x-axis of the curve y = (x + 2)³.
Thanks skipjack! As stupid as it sounds, I'm having difficulty of understanding the translations of cubic graphs. I understand the inflexion but when it comes to understanding horizontal, vertical and reflections. Is it sufficient enough to say that for example so so equation is a translation of +2 in the x-axis of the curve y=x^3 or so?

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: 20,370 Thanks: 2007 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 x-axis. 6. y = f(-x) $\ \ \,\,\,\ \ \$Reflected in the y-axis. 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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