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Graphing Polynomial Functions Using End Behavior, Zeros, and Multiplicities

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Learn how to graph polynomial functions using end behavior, zeros, as well as multiplicities in this video math tutorial by Mario's Math Tutoring. We discuss how to find the zero through factoring and the zero product property. We also discuss whether the graph is going up or down to the right using the leading coefficient test and the degree of the polynomial. Lastly we discuss what the graph of the polynomial looks like when the multiplicity of the zeros is 1, 2, 3, or more. We go through 3 examples to illustrate this concept.
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Опубликовано:

21 авг 2024

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Комментарии : 170

@blissbenson3163 3 года назад

Just spent two hours staring at a graph🙈. Your explanation saved my ass,now I can get some sleep. Thank you

@yasarhassan5803 3 года назад

Wake up

@silverpockets9 3 года назад

@@yasarhassan5803 nice

@hannahmyears8451 3 года назад

@Zaid Hank woah! You have to be desperate to make two fake accounts!

@jakevilla2309 3 года назад

@@hannahmyears8451 haha 😂

@lylemaximiliano8756 3 года назад

i dont mean to be off topic but does anybody know of a trick to log back into an instagram account? I stupidly forgot my account password. I would appreciate any help you can give me.

@thelastasolplayerrip7640 2 года назад

When you have to teach a class at 8, but pilot the starship enterprise at 9

@rafaelleuterio7900 2 года назад

broooo

@offthewall2017 2 года назад

Picard is the captain, he doesn't pilot the enterprise, that's the helmsman.

@cathystutler8359 2 года назад

@Romeo Sanchez It is a Star Trek reference.

@JayT0o 2 года назад

So much easier to understand than anyone else I've seen on RU-vid. Thank you.

@cognus3372 10 месяцев назад

Professor Leonard's videos are really full lectures, but I think he has the best balance between completeness and sheer skill at communicating concepts.

@sejintennant8542 Год назад

I'm doing precalculus homework and , this is the best tutorial out of anything I could find. Thanks a lot!😀

@JediKnight_Tot 2 месяца назад

Literally cried at 9:23 when Mario said, " ... to go on & pursue your dreams." Thank you 3000😊

@ataberdi2064 Год назад

Very clear and concise explanation. I love how you meticulously deep dive into tiniest things we confuse about. 🤩

@marianoperezromero3277 3 года назад

This man is a straight legend

@user-he6mg6kw2m 8 месяцев назад

I am from Ethiopia, and you are the best teacher and I like your learning method, and finally, thanks, it was very clear 👏

@MariosMathTutoring 8 месяцев назад

Thank you! 😃

@ThaoNguyen-yb6xq 9 месяцев назад

Thank you Mr. Mario! I can always count on you !

@jackiek1772 2 года назад

Brushing up for my exam tomorrow. Your videos are VERY helpful! Thanks! :)

@jerrysmith9780 3 года назад

I just found your channel a few days ago while looking for Trig help. We love your content and relaxed approach. You seem like a very decent guy. Thanks man.

@triciakruse9191 2 года назад

This is excellent. I am a math teacher and I fine this to be very well done!

@yourmathtutorvids 3 года назад

Thank you for the refresher!! Haven’t thought about polynomials in years 😅

@lovemorembasela6491 2 года назад

Oh I am Lovemore. It's the second time I am watching you teach and it's absolutely impressive how you do it.

@marryjoynapat7676 3 года назад

Thank you so much for this lecture, it was so reliable and helpful , especially in our situation right now that we can't go to school and do self studying............it just I'm so grateful, that I can sleep right now................

@penelopeperez9558 3 года назад

Wow, this was amazing, your techniques and tricks for association make it so easy to learn and understand. I didn't get it the way my teacher explained it so thanks for your videos!

@coolgirl-zd5gg 3 года назад

you are a lifesaver omg thank you!!!

@ForbiddenFroots 5 месяцев назад

When I tell you I have been through so many videos and trying to understand this for over two weeks and you explained it perfectly. You saved my life!!!!! I feel like crying

@MariosMathTutoring 5 месяцев назад

Glad to hear my video helped you!

@ForbiddenFroots 4 месяца назад

@@MariosMathTutoring Thank you. I still failed and I don’t think Algebra is for me. Which you could’ve been my professor 😪

@jamesbyrne6232 3 года назад

Respect the hustle man, good stuff

@cameronnelson6474 2 года назад

This is literally helping me take a placement test for alebra 2 in 2 months :)

@Aksafos 2 года назад

This vedio is really helping

@manavjotsinghbrar6304 8 месяцев назад

I am from Philippines/India thanks you for your help math is so hard but you make it a easier way thanks 😊

@MariosMathTutoring 8 месяцев назад

You're welcome 😊

@user-pl2kd9vm8z 6 месяцев назад

Thank you so much for this tutorial!! I’m taking a business math course and was struggling with this concept , but you have explained it so well and helped me make sense of it all . Bless you !

@MariosMathTutoring 6 месяцев назад

Glad it was helpful!…and thanks for the super thanks!!!

@taopinairlinesmathindustry9144 5 месяцев назад

Thank you, you have taught me the math class i missed today in 10 mins instead of one hour of math. I ❤ your videos

@MariosMathTutoring 5 месяцев назад

Glad my video helped you!

@yeoslovelyblu 9 месяцев назад

Tysm my tracher sucks at explaining all he does is put a problem on a board expect us to solve it when he hasnt even teached it, lifesaver

@jmi420 Год назад

Thanks!

@austinstoneman8257 Год назад

your examples are great. thanks

@stephanie9810 3 года назад

Thanks to this video I finally understand our lesson.

@SpookyButtz 2 года назад

Thank you for making this video, I used these when doing my math class and now I have all my math credits to graduate! Good luck to anyone reading this and is still doing their maths. It sucks but I know you can do it!!

@1cualtemoch970 6 месяцев назад

I really like your video. You really dissect the problem. Good job, teach!

@MariosMathTutoring 6 месяцев назад

Thank you very much!

@neelkhairnar1822 Год назад

Nice to see Oppenheimer teaching polynomials !!!!!!!

@nextgeninside 10 месяцев назад

lol

@augustineaboateng9707 2 года назад

Mario, you are so helpful, God will bless you forever. Please when the function is not in the factorized, what is the approach in graphing?

@user-no3gn5mu2v 3 дня назад

Thank you so much for sharing this!

@MariosMathTutoring 3 дня назад

You are so welcome!

@jacobebstein8838 3 года назад

You did better than my teacher. :)

@xiaosongwu6744 Год назад

Great video, thanks! Suggestion: in 2nd polynomials, it was written “- x^x = 0” well, -1 is actually the leading coefficient, not part of the first factor/term. In the video, it went on by multiplying -1 on both sides of the equation to get to x^x = 0, which is completely unnecessary and quite confusing. We just need to recognize -1 being the leading coefficient, to avoid the confusion.

@IsabelRodriguez-nv2ue 3 года назад

Thank you very much for creating these videos that help so much in understanding this material!!!!

@throwawaygmail860 2 года назад

mr mario you are brilliant thank you for your service

@AshalakVeerSingh Месяц назад

Nicely solved

@oliviap1201 Год назад

you are my savior !

@massielpekar39 9 месяцев назад

watched multiple videos and I was so confused, your video made so much sense! thank you!

@MariosMathTutoring 9 месяцев назад

Glad it helped!

@reynoldprajogo531 3 года назад

Thank you Mario for your explanation

@aryantiwari8982 2 года назад

The only mario helped me in study

@aqsashahzad4810 3 года назад

Thank you for this, it really helped

@prs901 3 года назад

tnx man u help me,i have a test tomorrow keep it up

@ta2010ist 4 месяца назад

Please add this question too. Write an exact equation for this polynomial function using the additional point provided. Assume all zeros are integers.

@Lostwolf16 2 года назад

Thank you, learning this for phase diagrams for differential equations because my precal teacher was terrible

@asmaazayan3130 3 года назад

You are really fantastic ❤ KEEP IT UP !!!

@ayarpireganyan5149 Год назад

Thanks Mario, this was so helpful!

@MariosMathTutoring Год назад

Glad it was helpful!

@NIPOON_nhoon_THOMPAT Год назад

Thank you teacher Mario.🙏☺🙏

@MariosMathTutoring Год назад

You are very welcome

@yourmom7196 3 года назад

Thank you so much for this, this will help me so much on my test!

@mariam_ah Год назад

THANK YOU SO MUCH

@joenkonziki7809 Год назад

Brilliant Teacher. 👌🏿👌🏿🙏🏿🙏🏿

@matthewdichigo 6 месяцев назад

Thank you so much for your knowledge as usual amazing teacher

@MariosMathTutoring 6 месяцев назад

You are very welcome

@Leeuuy 11 дней назад

Thanks

@afnancricket 11 месяцев назад

I love Mario

@fitquipltd6788 3 года назад

Thank you for an easy to understand explanation.

@emmasnyder8987 Год назад

thought maybe i was stupid but now i realize maybe my college professor isn’t the greatest at explanations 😃

@laisabuinimasi2154 2 года назад

Just discovered ur chanel n I learnt so much. Thanks

@edisonburger 6 месяцев назад

THANK YOU

@Aksafos 2 года назад

Impressive video

@andrewc736 3 года назад

Thank you everything was explained perfectly

@addisonmil4er 6 месяцев назад

U saved me I love you

@ketanchandra5593 2 года назад

This was great. Thanks!

@Songoku-dm4nd 11 месяцев назад

thanks teacher you good buddy

@kylinruiz71 Год назад

i wish i found you at the beginning of the semester

@joymurerwa5656 Год назад

Thank you so much for this!

@sarvaryusupov7108 2 года назад

Thank you very much 😊 for explaining

@Imperium32 3 года назад

Good sir you are giving me hope,thank u for this helpful video really appreciate it cause my modules are stressing me out

@fnafcoolguy5362 2 года назад

thank you

@s12mansoor78 Год назад

Thanks this video is very helpful for me ❤

@dorasilva9807 3 года назад

Saved my life thanks you 😭 ' .

@erikadahlqvist6545 3 года назад

Very good explanation Mario! Thanks for this :)

@Nxftqiue Год назад

Thank 🙏

@AstroKungfu 3 года назад

You explain this topic very well. When will you have precalc in your video lessons? They only go up to Algebra II...

@dusanexol7535 2 года назад

Thank you very much, teacher)

@BrightAcademy12 3 года назад

oh very well explained. thank it helped me

@erendemir9553 2 года назад

Thank you so much, it helped me so much

@mariamissa2458 3 года назад

thanks Mario!

@ryanbalthazor3698 2 года назад

love you mario!!! you rule

@jasminemaruquez9552 3 года назад

Thank you so much!

@a.sumido 3 года назад

I really love your vids! Thanks.

@ixchel8772 2 года назад

WHAT A GREAT VIDEOOOO!!! SOOO HELPFULL

@jnathan_7397 Год назад

Currently one am trying to stuff as much information into my brain for tomorrow

@jovi4872 3 года назад

If I can do something else than THANK YOU I won't missed it.

@danlemuellagazon6275 3 года назад

thank you very much!

@yoditgirma7213 3 года назад

Your the best, i've subscribed

@thegodofmarch2218 2 года назад

thanks jeff!

@janjoeydavenido9798 2 года назад

it is really healpful!!

@ibsaasamuel 4 месяца назад

teacher how contruct line tangancy to circle?

@SoyJeremiah 4 месяца назад

AWESOME

@MariosMathTutoring 4 месяца назад

Thanks 🤗

@treeme7252 2 года назад

Can you give us non factored example? I'm struggling hard with graphing those. As an example, x^4 + 2x^2 -4

@shaikhaalshahi7419 3 года назад

You’re the best

@saiashok28 10 месяцев назад

Hi Do you have video for finding local max/min and global max/min?

@MariosMathTutoring 10 месяцев назад

TI84 TI83 Finding Relative Maximum & Minimum ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-5zH9bPKrqO4.html

@crispymallows7075 3 года назад

you saved me in math i was failing so bad and your teaching really helped me THNKU SMMMM

@yarrowstudy3530 3 года назад

Sir plzzzzzz make video on lim h tend to 0 then (1)/e^-1/h

@naveedumair2677 3 года назад

For the last problem the graph looks like a W

@r.nunezz Год назад

Hey Mario, when you have a multiplicity of 3 why doesn’t it bounce off that point?

@MariosMathTutoring Год назад

Odd multiplicities go through, even multiplicities will ‘bounce’

@livinlife123 Год назад

in the first example, what is the point of the two in the front?

@MarleneBaugh 10 месяцев назад

The 2 infront is the leading coefficient which determines whether you go up or down to the right. If the leading coefficient is positive the graph goes up to the right. But if the leading coefficient is negative the graph goes down to the left eg. In a negative x Sq graph. The graph turns down. He this helps