Testing for Symmetry with Respect to the x-axis, y-axis, and Origin

This video goes through three examples: one testing for symmetry around the x-axis, one testing for symmetry around the y-axis, and one testing for symmetry around the origin.
#mathematics #algebra #maths
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[@kelleyheaton2111]

Oh my gosh, thank you. I am an older student, and I have never seen this stuff. I'm starting to lose hope. We started this today, and you explained it in a way I feel like I understand. It is amazing that people like you take the time to do this...you have no idea what it means to people like me. A million thanks!!

[@ColesWorldofMathematics]

You're welcome! Glad the video was helpful! Thanks for watching.

[@lateshiachilds3640]

Kelley Heaton same here its been awhile since ive been in school, im taking college algebra now. Im competing with twi high schoolers in my class....they get it, here i am 40 years old....i cant keep up and ut doesnt help when the math teacher make me feel like stupid for not getting this stuff.

[@ColesWorldofMathematics]

So glad the video was helpful! Be sure to check out the playlists that are on my channel. I've tried to group videos together by topic as well as by class title. I teach at both the high school level and college level, so I have videos that would cover most of the topics found in a college algebra class. Good luck!

[@tanveerkhan743]

Did she paid you to write that ? You don't have to answer

[@Alexehrh]

@@ColesWorldofMathematics if there way an equation that started with a negative x or y would I flip it or just keep it becasue it’s negative?

[@nickolascrousillat4265]

all i needed was this not a one hour lecture from my teacher.

[@ColesWorldofMathematics]

Glad the video was helpful for you - but sorry you sat through a one hour lecture.

[@FatimaKhan-zc5dg]

You explained it sooooo much better than my professor did in 6 minutes. Thank you

[@ColesWorldofMathematics]

Thanks! Glad my method helped you!

[@experiencethebeats4217]

I oftentimes find myself re-watching some of your videos. It definitely helps when reviewing for a test.

[@ColesWorldofMathematics]

So glad the videos are helpful for you! Thanks for watching. Please share with your friends.

[@Mineo5]

I so appreciate you making this video. It's been over 10 years since I've seen any of this and I understood it so quickly watching this!! You'll never know how many you have helped! Thank you!!

[@ColesWorldofMathematics]

Glad it was helpful!

[@juliawburn2352]

Thank you for the concise and organized explanation, everything makes total sense now. I love the neat way you explained on the paper!

[@ColesWorldofMathematics]

Thanks! Glad the video was helpful! Thanks for watching!

[@VansSkully]

I have a final for pre calculus for business tomorrow and I was really struggling with this concept. Thank you for the clear explanation!

[@ColesWorldofMathematics]

You're welcome! Glad it helped! Good luck on your final!

[@foothillfalcon14]

don't normally comment on these but good job... super simple and straight to the point with clear examples! Thank you

[@ColesWorldofMathematics]

Thank you so much! Glad you took the time to comment! Thanks for watching.

[@sabrinadavis2941]

Thanks so much for this easy explanation. You were straight to the point. That helped so much.

[@ColesWorldofMathematics]

+Corliss Rich You're welcome! I enjoy making videos that help people understand math!

[@Cloud_Nine_E]

This was so on-point, simple, and short. Bunch of thanks. 👌

[@ColesWorldofMathematics]

You bet! 👍🏻

[@559caliPoros]

Bless your soul and the souls of all educators that make it look easy

[@ColesWorldofMathematics]

Thank you so much.

[@maurosgarage]

thanks for the video.. You explained it much more clear than my teacher and got your point across in a fraction of the time that my algebra teacher did.

[@ColesWorldofMathematics]

Thanks! Glad it helped you! Thanks for watching!

[@allthingspey4702]

Thank you sooo much! This video helped me on a problem that I was stuck on for the longest and made it soo simple

[@ColesWorldofMathematics]

So glad the video was helpful for you! Be sure to check out the rest of my channel, everything is organized by playlists.

[@eboaktree]

Thank you so much for the clear and concise explanation on testing symmetry-algebraically. Very helpful!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@rubenmercado3326]

I agree with mauro, this video explained it so well in a fraction of the time. thanks

[@ColesWorldofMathematics]

You're welcome! Thanks for watching. Please share with your friends.

[@Nicro328]

Have a midterm this coming Thursday and was a little bit fuzzy on this subject. Thank you for the clear and concise presentation!

[@ColesWorldofMathematics]

You're welcome! Hope you did well on the midterm. Thanks for watching.

[@yaelisakov4477]

I love how clear you are! thank you :)

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@CodeIsLife101]

Ah, that was beautiful. Straight forward and clear. Thank you.

[@ColesWorldofMathematics]

You're welcome! Glad it was easy to understand! Thanks for watching.

[@humorlesspuma4839]

Thank you for explaining this is three different equations it really helped me follow along with your method and made thigns easier. I went to my tutor, professor and class tutor and didnt understand but you explained it in simplier terms. Thanks

[@ColesWorldofMathematics]

You're welcome! I'm so glad the video was helpful for you! Thanks for watching.

[@dougjenkins7311]

Excellent job explaining this topic! Two thumbs up.

[@ColesWorldofMathematics]

Thanks! Please share with your friends.

[@yoink2454]

I just got off work and there’s a math test tmrw. This is amazingly easy to understand, thank you

[@ColesWorldofMathematics]

So glad the video helped you out! Thanks for watching and commenting.

[@carmelssss]

How did you just divide how by -1 for the origin on both sides without considering the denominator?

[@tyru2]

This was so helpful, I appreciate it lot.

[@prinzecesartonares9332]

can you uplaod how to graph these quation? and how to shade in the region?

[@ricardoperez2039]

Amazing!! Thank you for the walk through!!

[@ColesWorldofMathematics]

You bet! Thanks for watching.

[@abrynnb]

Thank you so much for posting this video. I missed one day of /my Discrete class and this is what we cover. I came in the next day and had no clue what we were doing. This helped me so much!

[@ColesWorldofMathematics]

+abrynnb You're very welcome! My main purpose for posting math videos is to help students. It's just a few extra examples that hopefully fills in the missing gaps! Good luck the rest of the semester!

[@Jomariepng]

+Cole's World of Mathematics Thank you for this video! I am in 4th grade math excel and I was going to get put back in regular math if I didn't know this. I am still in math excel today!

[@ColesWorldofMathematics]

Jordi Pop Glad I could help! Good luck with Math Excel.

[@travis216]

This video was very helpful! Thank you so much!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@Kawaiigirl4.0]

What if you have an absolute? Like y= the absolute of x-5. I got that only one of the y-axis work What do I do?

[@leiamelaku3898]

You are so helpful thank you so much I really appreciate this video. Definitely subscribing!!!

[@ColesWorldofMathematics]

Awesome! That’s great. Be sure to check out the playlists on my channel. That’s probably the easiest way to find what you are needing for class.

[@supremedom1nate]

Thank you so much! I was totally lost because my professor gave a horrible example like y=x cubed and it made no sense at all. now I completely understand.

[@ColesWorldofMathematics]

Glad this helped.

[@trantu7202]

thanks to your video so much , the way you explained helped me so much in understanding this lesson . I got the hard time in class . ❤❤

[@ColesWorldofMathematics]

Glad it helped you! Thanks for watching!

[@willdavis7846]

I watched this video for 2 minutes and i am now able to tell you the answer without doing any math. Im learning all college algebra from different youtube math people

[@ColesWorldofMathematics]

Good job! Thanks for watching.

[@zeroblade3717]

Would the example in the middle be a symmetry of origin

[@megamindblue1732]

Thank you so much. Conscience and educational.😊

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@meazi01]

Very understandable lecturing video. Thank you

[@ColesWorldofMathematics]

Thanks so much for the positive comment! 👍😀

[@mwerensteijn]

Thanks a lot, great explaination!

[@ColesWorldofMathematics]

Glad you enjoyed it!

[@sirisaacnewton2186]

Thanks! Great video!

[@ColesWorldofMathematics]

You bet!

[@adrian8729]

Easy and Clear, im proud.

[@ColesWorldofMathematics]

Thanks!

[@tamimlkerba2366]

Thank you, it was super helpful

[@ColesWorldofMathematics]

Glad it was helpful for you!

[@toptentruth]

Very helpful

[@skylar011]

It would have been very helpful to have examples of polar equations, like the one I'm trying to figure out now, r=9+8sintheta.

[@bakedflan2155]

Thank you so much! This came in handy.

[@ColesWorldofMathematics]

I'm so glad! Thanks for watching.

[@monkeys123lol]

Wow awesome explanation!

[@ColesWorldofMathematics]

Glad you liked it!

[@pankajkumawat3505]

Tq mam it is too helpful..

[@jacobrye3949]

That’s not how it says in my pre cal book it says for the y axis you would also have to multiply both sides by 4

[@u_d_m]

Very good Explanation!!!🥰

[@ColesWorldofMathematics]

Thank you! 😃

[@Johnston1]

Thank you!

[@adcreativedesign6]

if these possible for a functio not exist symmetric

[@abigailholdsclaw6997]

Thanks for the helpful video!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching!

[@Neha-oi3fv]

Thank you so much! This really helped on my hw.

[@ColesWorldofMathematics]

Glad it helped!

[@sannasamateh7582]

May u be a president of the world math

[@phoebesay]

Thank you so much for this video.

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@jonathanc1084]

What happens when you have something like this x^2 absolute value of y =8 ? can you do the same procedure to see if the symmetry ?

[@ColesWorldofMathematics]

The process is the same. Substitute in the negative x's or y's, simplify, and check for a match.

[@deltaexplorer47]

WOW THANK YOU... it is much easier than graphing !!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching. Glad the video was helpful!

[@benatchley4928]

Excellent!

[@ColesWorldofMathematics]

Thanks.

[@muhammadsaeed3820]

Very helpful vedio ...thanks

[@ColesWorldofMathematics]

You’re welcome! Thanks for watching & commenting!

[@sterlingteall3462]

That was very helpful.

[@ColesWorldofMathematics]

Glad to hear!

[@genevieveantwi4244]

love this video so helpful! !!!

[@ColesWorldofMathematics]

So glad it was helpful for you! Thanks for watching!

[@srishtigulrajani764]

Amazing explanation 😍 thankyou mam❤

[@ColesWorldofMathematics]

Most welcome 😊

[@anweshapalai3477]

Oo it's really helpful... thanks...🤗

[@ColesWorldofMathematics]

Most welcome 😊

[@smdjose2400]

hey im a sophmore in hs and i just need to know does the equation have to be y= or can it be in any order

[@ColesWorldofMathematics]

It can be in any order.

[@rozhsabah3631]

I understood very well thanks alot for your explanation

[@ColesWorldofMathematics]

Glad it helped.

[@OHMSdev]

thank you, your handwriting is very nice btw.

[@ColesWorldofMathematics]

Thank you so much 😀

[@jasomega2446]

Thank You!

[@ColesWorldofMathematics]

You Bet! Thanks for commenting.

[@mosesnavarrette5388]

Thank you ,your a gem .🙂

[@ColesWorldofMathematics]

Glad to help

[@saary3243]

The best ever, thank you

[@ColesWorldofMathematics]

You're welcome! Thank you so much for watching.

[@NataliaTatyana]

This was really helpful!

[@ColesWorldofMathematics]

That's great. I'm glad it was helpful! Thanks for watching. 👍

[@acemasakayan2738]

If the given is a -x do you turn it into a positive x? Or keep it into a -x since you have to change it to a -x getting the symmetry to the Y axis?

[@thedarklord3523]

you would turn it into a positive x.

[@forthelasttime4005]

"Therefore, it remains a *Nay-ge-teeve* x to the third power"

[@ColesWorldofMathematics]

I definitely pronounce certain words weird. lol My students tell me that all the time. 🙂

[@forthelasttime4005]

@@ColesWorldofMathematics Thanks for the help though. You made it super clear 👌🏻👌🏿

[@user-or4xu3pw9i]

why is -y squared still y2 but -x squared is -x squred

[@newlaguinaldo1280]

Thank you sosososososo much!!!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@kingatandinsherpa7063]

Perfect !!!

[@ColesWorldofMathematics]

Thanks.

[@diamonds7436]

On example 3, does diving by -1 affect the positive 5?

[@AB-ft7ng]

Nope! Even though it looks like the negative is only attached to the x, it’s actually part of the whole fraction, including the denominator. So another way to look at it would be: -y = -( x / x²+5 ) So now when you divide both sides by -1 you can see it will only get rid of the entire fraction’s negative sign, NOT affecting the numerator and denominator separately. I know this comment is a year old, but figured I’d still answer for anyone who’s thinking the same thing and still needs it lol

[@bhopstraining]

@@AB-ft7ng I had the same question, so thanks :)

[@evenismail6745]

@@AB-ft7ng woah thanks I totally forgot that ❤️

[@claudiapatriciacuartasagui3381]

Claudia Cuartas MAC1105 Monday, Wednesday 9:30am-10:45 Professor Hearn "We can see the y's match, the 4's match, but the x to the third does not... I can conclude that the cubic equation is not symmetrical to the y-axis. 3:22

[@Kelalasdemonx]

why did it not become +y

[@kelskels1025]

thanks queen

[@ColesWorldofMathematics]

You bet!

[@ZeeshanAbbasiplanz]

Thanks

[@11dheerajkumar81]

very nice explained

[@ColesWorldofMathematics]

Thanks....and thanks for watching.

[@Shortsx945]

I think we have to replace -x on both sides

[@NirajMandal-nr5ir]

Thank you❤

[@ColesWorldofMathematics]

You're welcome 😊

[@mycool2512]

THANK YOU

[@ColesWorldofMathematics]

You're welcome. Thanks for watching & commenting.

[@laurensweat767]

How does (-y)^2 become y^2 If you use the SQUARE to SQUARE IT then wouldn't it just be y? How in the world is the square still there after you used it to simplify???

[@ColesWorldofMathematics]

(-y)^2 means -y times -y. Showing the exponents & coefficients, you have -1y^1 times -1y^1. When multiplying like bases, you add the exponents (and you also just multiply the coefficients like normal), so (-y)^2 = -1y^1 times -1y^1 = 1y^2 or just y^2.

[@husseinaldabbagh424]

thanks sooo much!

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@crimplepick3631]

you did what my teacher couldn't accomplish thank you

[@ColesWorldofMathematics]

So glad I was helpful for you! Thanks for watching!

[@adnansajid1708]

Queen 👑❤

[@mdmaleque7254]

Thanks a lot

[@ColesWorldofMathematics]

You’re welcome!

[@user-jm7zy2cr3y]

Thankyou ❤

[@ColesWorldofMathematics]

You're welcome 😊

[@nagendra5529]

thanks it really helped

[@ColesWorldofMathematics]

So glad the video was helpful for you! Thanks for watching.

[@xlajimex]

thank you!!

[@ColesWorldofMathematics]

You’re welcome!

[@JP-hu8ow]

Thank you

[@ColesWorldofMathematics]

You're welcome!

[@greyeyedone_2119]

Thank you for this video it helped a great deal.....🧠📕📗🤓📘📚🔬👩🏽‍⚕️

[@ColesWorldofMathematics]

So glad the video was helpful! Thanks for watching.

[@Itslalajamera]

Awesome 😃

[@ColesWorldofMathematics]

Thanks!

[@adcreativedesign6]

how

[@Mroi1]

Thank you very much

[@ColesWorldofMathematics]

You're welcome! Thanks for watching.

[@sanjanagrover7436]

THANK U MA'AM LOVE FROM INDIA!!

[@ColesWorldofMathematics]

❤️👍🏻

[@rabindrarout6769]

Thanks mam.... your voice is so nice

[@ColesWorldofMathematics]

Thanks so much!

[@classychick2100]

does the equation have to start with y= to test it?

[@ColesWorldofMathematics]

No, the equation does not have to start with y = to test it.

[@classychick2100]

okay thanks!

[@lara-og9gl]

Thanks a looot

[@ColesWorldofMathematics]

You're welcome!

[@daily_islamic5368]

Thanks 👍👍👍👍👍👍

[@ColesWorldofMathematics]

You're welcome!

[@-smp-scientificmethodpersp838]

So symmetric with respect to the x-axis is the same as simply reflected to the x-axis?

[@ColesWorldofMathematics]

If I understood what you wrote, yes, you are correct.

[@-smp-scientificmethodpersp838]

@@ColesWorldofMathematics what I meant was that they mean the same thing, so I guess I got that right?

[@ColesWorldofMathematics]

Yes, they mean the same thing. 😊👍🏻