Graphing Higher-Degree Polynomials: The Leading Coefficient Test and Finding Zeros

By now, graphing lines seems trivial, and even graphing quadratics is a piece of cake. But what about higher-degree polynomials like cubics, quartics, and quintics? And even higher than that? It might seem quite daunting, but there are some handy tricks that will help you graph even these very complex functions. These involve using the leading coefficient test to discern the end behavior of the function, as well as plotting zeros and assessing their multiplicities in order to get a rough sketch of the function. It's not as bad as it sounds, check it out!
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Пікірлер: 130

  • @kevindeng5781
    @kevindeng57814 жыл бұрын

    I have a test tomorrow, thank you so much...

  • @muutrich

    @muutrich

    3 жыл бұрын

    @Latifa Alawadhi this comment was made 9 months ago man, the guy passed the course already lmfao

  • @ciaraboone

    @ciaraboone

    3 жыл бұрын

    mine is in an hour 😳

  • @Sam-fv4xq

    @Sam-fv4xq

    3 жыл бұрын

    @@ciaraboone mine in 3 hours

  • @vapecat17yearsago85

    @vapecat17yearsago85

    3 жыл бұрын

    Nah I ALREADY did the test. Teacher wants me to show work so I put this LMFAO

  • @Aaradhya9797

    @Aaradhya9797

    3 жыл бұрын

    @@ciaraboone soo sad...🤣

  • @sarag.2090
    @sarag.20903 жыл бұрын

    Thank you for explaining everything better than my teacher lmao

  • @mesumabbas9481

    @mesumabbas9481

    3 жыл бұрын

    Yeah those hearts are only restricted to beauties.

  • @a.henderson22
    @a.henderson224 жыл бұрын

    tthank you so much for making this video I really had no idea where to start with these problems

  • @santialterman3066
    @santialterman30663 ай бұрын

    This is by far the best channel for explanations. I love how clear and visual you are, plus you answer the "whys" of math (to get the max we need calculus). Thank you

  • @lastweek438
    @lastweek4384 жыл бұрын

    thanks professor for making this video.it has further motivated me in loving the algebra

  • @justinac6465
    @justinac64654 жыл бұрын

    thank you so much! I am currently studying for a math cst test and this helped clear up some difficulties I had with higher order polynomials! thank you

  • @Aaradhya9797

    @Aaradhya9797

    3 жыл бұрын

    Hii

  • @al-farabinagashbayev5403
    @al-farabinagashbayev54036 жыл бұрын

    Hi, nice video. I recommend you also to explain how to plot polynomials of multiple variables. It would be great)

  • @NickHope
    @NickHope2 жыл бұрын

    The equation in the comprehension question should be x^4 + 5x^2 + 4 = y because x^4 + 5x^2 + 4 = 0 does not contain y, and is only used to find the x-intercepts; it is not the equation that we actually want to graph, which must contain y for the given answer.

  • @agenericboringhomosapien8108

    @agenericboringhomosapien8108

    2 жыл бұрын

    Right sir

  • @TheTemporaryLasters

    @TheTemporaryLasters

    Жыл бұрын

    it is a hidden quadratic

  • @gianfrancobruschetta2423
    @gianfrancobruschetta2423 Жыл бұрын

    Hi, what's the solution of the factoring? thanks.

  • @russiandog0732
    @russiandog07322 жыл бұрын

    Thank you very much, This is so helpful.

  • @mugiwaranoluffy4656
    @mugiwaranoluffy4656 Жыл бұрын

    This guy is a big help ❤️

  • @rajeshbeniwalbeniwal6001
    @rajeshbeniwalbeniwal60013 жыл бұрын

    Finally......., I got it ....., Thanks a lot sir😍😍

  • @Soumyadip_Pal
    @Soumyadip_Pal6 жыл бұрын

    Hi there, would you like to make a series about Elliptic Curve Cryptography (ECC) in future? I would love to learn from you.

  • @user-zo3wy4we3t
    @user-zo3wy4we3t5 жыл бұрын

    Will you have cheat sheet pdfs that cover everything that can be used to be printed out or saved? Or do i just have to take notes on the video?

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    I’ve thought about doing PDFs but it’s a lot of work, I suggest just taking full screen screenshots to make your own little slides.

  • @gabriel9668
    @gabriel96684 жыл бұрын

    Thank you!

  • @joshyanza6130
    @joshyanza61303 жыл бұрын

    Thank you very much professor

  • @larssalembier7790
    @larssalembier77904 жыл бұрын

    There is a small error in the video: when he says that you can also use the y-intercept, he puts the y-intercept of the function somewhere around -2/3, but if you actually calculate the y-intercept by replacing all x'es with a 0, you can see that the y-intercept is (0, -3), so the drawing is incorrect, the extrema of the function are way more outspoken.

  • @doctorbolsen

    @doctorbolsen

    3 жыл бұрын

    Yep

  • @ha5541

    @ha5541

    2 жыл бұрын

    Yeah

  • @kexcro8972

    @kexcro8972

    2 жыл бұрын

    He’s not wrong the x and y axis don’t have to follow the same scale.

  • @agenericboringhomosapien8108

    @agenericboringhomosapien8108

    2 жыл бұрын

    Yup...

  • @shubhamkukreja96
    @shubhamkukreja965 жыл бұрын

    Thanks for clearing my concepts of this topic Very nice method of teaching

  • @wdekeizer
    @wdekeizer2 жыл бұрын

    thank you this is exactly what i needed

  • @felipeshannkarln.121
    @felipeshannkarln.1213 жыл бұрын

    Very infotmative. Impressive. I'll be subscribing

  • @guidopierdomenico5108
    @guidopierdomenico51082 жыл бұрын

    i understood everything except for the factorization of the comprehension exercise, can someone explain it to me? plz?

  • @markstephenbueno4314
    @markstephenbueno43143 жыл бұрын

    I have a test later. Thank you!

  • @ninjakiwigames5418
    @ninjakiwigames5418 Жыл бұрын

    Holy shit you explained this so perfectly my math teacher could never

  • @user-wg2rh6sb7c
    @user-wg2rh6sb7c Жыл бұрын

    professor, can you help me please the how to compute the apparent weight of a 60kg student standing inside a lift while he accelerates 2m /s square down ward, at rest and 2m /s square up ward, Just its formula pease.

  • @amandaneves435
    @amandaneves435 Жыл бұрын

    Thank you, sir.

  • @sislol3685
    @sislol36853 жыл бұрын

    Can someone explain me the comprehension quiz

  • @sina1436
    @sina14362 жыл бұрын

    i see 2 zero does it get multiplied and gives 4?

  • @Joseph-xs2mo
    @Joseph-xs2mo3 жыл бұрын

    6:49 KZread’s red line is jumping out

  • @dhayn_gwyn
    @dhayn_gwyn Жыл бұрын

    thank you, god of math

  • @joy_takoyakie
    @joy_takoyakie3 жыл бұрын

    this is way better than going to school💕 I literally understand it😎 thanks again 😄

  • @eyosuga3809
    @eyosuga38094 жыл бұрын

    this tutorial is Damn good I think im' get at least check in this part of the quiz tomorrow

  • @foodisgood7607

    @foodisgood7607

    3 жыл бұрын

    shut up

  • @doctorbolsen

    @doctorbolsen

    3 жыл бұрын

    @@foodisgood7607 Shut up

  • @funtime6225
    @funtime62253 жыл бұрын

    you can get the y values by plugging the x'es in the equation.

  • @lynevertayzon8638
    @lynevertayzon86383 жыл бұрын

    Thankyou!

  • @sangyunlee4523
    @sangyunlee45233 жыл бұрын

    YOU ARE THE BEST -from KICS

  • @buica2566
    @buica25663 жыл бұрын

    Superb.

  • @GmyB0202
    @GmyB02025 жыл бұрын

    If all math teachers were like him or has his attitude I think many students wont need to watch this type of videos.

  • @chotuu5400
    @chotuu54002 жыл бұрын

    Thanks sir

  • @HarshVardhan-wf5lu
    @HarshVardhan-wf5lu3 ай бұрын

    thank u for that saved my time

  • @ayoubelghazi8918
    @ayoubelghazi89183 жыл бұрын

    can someone explain to me how he resolved the comprehension equation? nvm I got it

  • @zorobabe6258
    @zorobabe62583 жыл бұрын

    Thankyou so muchhhh

  • @MIHNU2023
    @MIHNU20232 жыл бұрын

    Thank you, Math Jesus

  • @user-tc5gm8nv2i
    @user-tc5gm8nv2i7 ай бұрын

    you just explained everything my math teacher failed to do in a semester lol. thanks

  • @victorzoma2749
    @victorzoma27493 жыл бұрын

    Great explanations But 😄😄 how did you study on your own to understand at such deeper level?!!😁😁😁(aka your study tricks)

  • @SephBustamante
    @SephBustamanteАй бұрын

    has to be y=4 specifically on x=0 on the comprehesion test or nah? and how do i get 4 do i just plug in 0 on the x

  • @SephBustamante

    @SephBustamante

    Ай бұрын

    like on the (x+1)(x-1)(x+2)(x-2) because if you plug 0 in you do get +4

  • @relaxee5159
    @relaxee51595 жыл бұрын

    thank you, I have an algebra II test tomorrow and you probably saved me a failing grade.

  • @yukimaru4667
    @yukimaru46672 жыл бұрын

    I can't find the zeroes in the given question using the synthetic division. Can someone pls give a method to find the zeroes

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    2 жыл бұрын

    rational roots test, it's covered in my tutorial on synthetic division

  • @vedansh7010

    @vedansh7010

    2 жыл бұрын

    You can also use the quadratic formula just rearrange it like this and you would be able to find x^2. (x^2)^2 - 5(x^2) + 4 = 0

  • @yukimaru4667

    @yukimaru4667

    11 ай бұрын

    Thank you

  • @ninjakiwigames5418
    @ninjakiwigames5418 Жыл бұрын

    Ofc Professor Dave has a video on every topic I need to study. (insert a blessing from the lord meme here)

  • @zavryonthegrind6329
    @zavryonthegrind6329 Жыл бұрын

    watching while taking the test

  • @princessmaedesacula0820
    @princessmaedesacula08203 жыл бұрын

    I'm literally answering my module and I visit the link reference on our topic. Thank you so much for explaining. I had learned a lot. I can share this to my very late teacher who doesn't spend time discussing that is why I don't know anything without this video. HAHAAHAAHA

  • @foggedmirror3973
    @foggedmirror39734 жыл бұрын

    How did you factor? I don't understand how you got the (x+3)(x+1)(x-1) at 3:43 I know how to factor but this is confusing me a little. 😩

  • @eneu9069

    @eneu9069

    4 жыл бұрын

    Trinity Lugo x^3+3x^2-x-3 Split in two pieces x^3+ 3x and -x-3 Factor each x^2( x+3) and -1(x+3) Now combine (x^2-1)(x+3) Factor x^2-1 X+1 x-1 Now you have x+3 x-1 x+1

  • @foggedmirror3973

    @foggedmirror3973

    4 жыл бұрын

    @@eneu9069 alright, i can understand that a bit. Hopefully I can apply that to what I'm doing. 😓 Thank you so much for the clarification.

  • @eneu9069

    @eneu9069

    4 жыл бұрын

    Trinity Lugo yea np we’re all here for help

  • @TheFirstNamelessOne

    @TheFirstNamelessOne

    4 жыл бұрын

    The method is factoring bu grouping.

  • @ict12-3a_aranetarannyb.2

    @ict12-3a_aranetarannyb.2

    3 жыл бұрын

    @@eneu9069 8:30 in this one a same procedure of it? kinda confuse

  • @allenlobrigas7154
    @allenlobrigas71546 ай бұрын

    I have a test later and im gonna clutch it

  • @AldreineMAlpas
    @AldreineMAlpas9 ай бұрын

    Uh when i tried to make the zeros in the checking comprehension its (x + 1)(x + 4i)

  • @mudalad1215

    @mudalad1215

    6 ай бұрын

    its a negative 5 bro

  • @biancafaith7569
    @biancafaith7569 Жыл бұрын

    I still don't get it. How would you know how high will the turning point be till it goes back down or up?

  • @lena_utkina

    @lena_utkina

    Жыл бұрын

    we're dont. thats bc it's just sketch

  • @shivanshuawasthi2485

    @shivanshuawasthi2485

    Жыл бұрын

    it's just a rough idea about the graph of polynomial

  • @ronycb7168
    @ronycb71689 ай бұрын

    I got my mistake made a mistake to consider the zeros to be even multiplicty thanks for the video

  • @tGoldenPhoenix
    @tGoldenPhoenix2 жыл бұрын

    Done.

  • @bullfrag4290
    @bullfrag42902 жыл бұрын

    i didnt knew you explain math problems

  • @g02balitakarylleleonec.34
    @g02balitakarylleleonec.343 жыл бұрын

    3:46 How did we get (x+3)(x+1)(x-1)=0?

  • @alyzaacierto5868

    @alyzaacierto5868

    3 жыл бұрын

    factors of 3x2

  • @mudalad1215

    @mudalad1215

    6 ай бұрын

    3 times 1 times -1 is 3, and -3

  • @kristoffer1085
    @kristoffer10853 жыл бұрын

    thank you math jesus

  • @johnvaldez6722
    @johnvaldez67222 жыл бұрын

    I don't mean to be pedantic here, but if you graph the equation shown at 8:18, x^4 - 5x^2 + 4 = 0, you're going to end up with four vertical lines with x-intercepts at x={-2,-1,1,2}. It seems like what you are really asking your students to do is sketch the graph of f(x) = x^4 - 5x^2 +4.

  • @manjupatil4717
    @manjupatil47173 жыл бұрын

    Nice intro

  • @mrdmajor
    @mrdmajor4 жыл бұрын

    "If you're confused, watch this clip one more time" 0:00 "If you're confused, watch this clip one more time" 0:00 "If you're confused, watch this clip one more time" 0:00 "If you're confused, watch this clip one more time" 0:00 "If you're confused, watch this clip one more time" "What is up guuuuuys? I decided to become a KZread 'content' creator!" 😂😭

  • @brenazelda224
    @brenazelda224 Жыл бұрын

    Ty ^v^ again

  • @brenazelda224

    @brenazelda224

    Жыл бұрын

    for explains to me

  • @shhidayeasmin6147
    @shhidayeasmin61475 жыл бұрын

    Can you explain maxima and minima by using calculus

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    yes i have a tutorial on that! somewhere in the calculus section, has to do with second derivatives

  • @jurisenpaiikun1042
    @jurisenpaiikun10423 жыл бұрын

    thanks math jesus

  • @ajprincessderek6229
    @ajprincessderek62293 жыл бұрын

    Lmao I'm watching to learn for the test and the example is the same on the test I was looking for an explanation but I got the answer lolololol

  • @samuelcrisolo6080
    @samuelcrisolo60803 жыл бұрын

    It doesn't make any sense to me. 😵. Even though, thank you for teaching.

  • @ignacioleikis1784
    @ignacioleikis17842 жыл бұрын

    Is it cheating if I use a graphing calculator?

  • @carultch

    @carultch

    Жыл бұрын

    Depends on who's asking you to produce a graph of the equation.

  • @kaileybump4298
    @kaileybump42984 ай бұрын

    I wish you were my professor lol

  • @senzuicodm6901
    @senzuicodm6901 Жыл бұрын

    thank you polynomial jesus

  • @Asian_Boii
    @Asian_Boii4 ай бұрын

    Me writing this comment to come back and tell myself the grade I got

  • @xama5x.

    @xama5x.

    Ай бұрын

    How much u got?

  • @biggestloseroftheday2598

    @biggestloseroftheday2598

    Ай бұрын

    yeah how much did this guy get

  • @Asian_Boii

    @Asian_Boii

    Ай бұрын

    @@xama5x. Oh yeah i forgot about this lol, got a solid 85% and ended my class with an A: 89.53 grade average!

  • @xama5x.

    @xama5x.

    Ай бұрын

    @@Asian_Boii congratulations

  • @mosyotark1748
    @mosyotark17489 ай бұрын

    oh no 4:54

  • @nerinedesu
    @nerinedesu3 жыл бұрын

    I'm so dumb, i still don't get it...

  • @bigbootybraxyn9801
    @bigbootybraxyn98012 жыл бұрын

    😃

  • @hackdog1258
    @hackdog12583 жыл бұрын

    Long hair Beard Helping people Jesus is that you?

  • @AlessandroZir
    @AlessandroZir2 жыл бұрын

    ❤️❤️🙏🙌

  • @mmooonnoor6502
    @mmooonnoor65022 жыл бұрын

    ياريت تتاكدوا من جواز حكم وضع الموسيقى او الاغاني ع مقاطعكم عشان تتجنبوا الوقوع بالاثم وشكرا لكم ربي يحفظكم

  • @ochna000
    @ochna0003 жыл бұрын

    yaann yaannnnn

  • @ikari3394

    @ikari3394

    3 жыл бұрын

    YANYANYAN

  • @samalexies

    @samalexies

    3 жыл бұрын

    Yanyanyan

  • @samalexies

    @samalexies

    3 жыл бұрын

    Module pa nga

  • @xin6341
    @xin63412 жыл бұрын

    Thanks Jesus

  • @tacoexpressSEEDEEholeeveryones

    @tacoexpressSEEDEEholeeveryones

    2 жыл бұрын

    jeeeehehehehehe an an an an

  • @lawrenceleones2326
    @lawrenceleones23263 жыл бұрын

    Math Jesus

  • @NinosEndlessVlogs
    @NinosEndlessVlogs4 жыл бұрын

    what the fuck im failing tomorrow

  • @darrenvinculado4293
    @darrenvinculado42933 жыл бұрын

    I can't understand a single thing

  • @faithelias2798
    @faithelias27982 жыл бұрын

    God loves you and he wants to save everyone, but in order for him to do that, you need to repent and be baptized. Also share his gospel with everyone you come in to contact with and keep his commandments 🙏🏾😘

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    2 жыл бұрын

    This is a math tutorial, sweetie.

  • @Teiwaz111

    @Teiwaz111

    2 жыл бұрын

    @@ProfessorDaveExplains Math loves you and wants to save everyone, but in order for math to do that, you need to revise and be educated. Also share this knowledge with everyone you come in to contact with and keep science alive 🙏🏾😘 There, fixed it for you 👍

  • @tacoexpressSEEDEEholeeveryones
    @tacoexpressSEEDEEholeeveryones2 жыл бұрын

    men should only wear short hair

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    2 жыл бұрын

    People don't "wear" hair, bud.

  • @designingworld6611

    @designingworld6611

    2 жыл бұрын

    @@ProfessorDaveExplains 👏👏