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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[@kevindeng5781]

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

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

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mine is in an hour 😳

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@@ciaraboone mine in 3 hours

[@vapecat17yearsago85]

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

[@Aaradhya9797]

@@ciaraboone soo sad...🤣

[@sarag.2090]

Thank you for explaining everything better than my teacher lmao

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Yeah those hearts are only restricted to beauties.

[@santialterman3066]

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

[@a.henderson22]

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

[@lastweek438]

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

[@justinac6465]

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]

Hii

[@al-farabinagashbayev5403]

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

[@mugiwaranoluffy4656]

This guy is a big help ❤️

[@joshyanza6130]

Thank you very much professor

[@rajeshbeniwalbeniwal6001]

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

[@russiandog0732]

Thank you very much, This is so helpful.

[@gabriel9668]

Thank you!

[@shubhamkukreja96]

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

[@wdekeizer]

thank you this is exactly what i needed

[@NickHope]

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]

Right sir

[@TheTemporaryLasters]

it is a hidden quadratic

[@markstephenbueno4314]

I have a test later. Thank you!

[@amandaneves435]

Thank you, sir.

[@felipeshannkarln.121]

Very infotmative. Impressive. I'll be subscribing

[@dhayn_gwyn]

thank you, god of math

[@ninjakiwigames5418]

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

[@larssalembier7790]

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]

Yep

[@ha5541]

Yeah

[@kexcro8972]

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

[@agenericboringhomosapien8108]

Yup...

[@GmyB0202]

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

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

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6:49 KZbin’s red line is jumping out

[@joy_takoyakie]

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

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YOU ARE THE BEST -from KICS

[@eyosuga3809]

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

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shut up

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@@foodisgood7607 Shut up

[@HarshVardhan-wf5lu]

thank u for that saved my time

[@lynevertayzon8638]

Thankyou!

[@funtime6225]

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

[@buica2566]

Superb.

[@chotuu5400]

Thanks sir

[@relaxee5159]

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

[@MIHNU2023]

Thank you, Math Jesus

[@user-zo3wy4we3t]

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]

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.

[@zorobabe6258]

Thankyou so muchhhh

[@gianfrancobruschetta2423]

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

[@user-tc5gm8nv2i]

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

[@ninjakiwigames5418]

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

[@guidopierdomenico5108]

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

[@tGoldenPhoenix]

Done.

[@victorzoma2749]

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

[@princessmaedesacula0820]

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

[@zavryonthegrind6329]

watching while taking the test

[@sislol3685]

Can someone explain me the comprehension quiz

[@user-wg2rh6sb7c]

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.

[@allenlobrigas7154]

I have a test later and im gonna clutch it

[@sina1436]

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

[@mrdmajor]

"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 KZbin 'content' creator!" 😂😭

[@ronycb7168]

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

[@SephBustamante]

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]

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

[@bullfrag4290]

i didnt knew you explain math problems

[@yukimaru4667]

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]

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

[@vedansh7010]

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]

Thank you

[@foggedmirror3973]

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]

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]

@@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]

Trinity Lugo yea np we’re all here for help

[@TheFirstNamelessOne]

The method is factoring bu grouping.

[@ict12-3a_aranetarannyb.2]

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

[@ayoubelghazi8918]

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

[@Asian_Boii]

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

[@xama5x.]

How much u got?

[@biggestloseroftheday2598]

yeah how much did this guy get

[@Asian_Boii]

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

[@xama5x.]

@@Asian_Boii congratulations

[@johnvaldez6722]

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.

[@biancafaith7569]

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]

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

[@shivanshuawasthi2485]

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

[@shhidayeasmin6147]

Can you explain maxima and minima by using calculus

[@ProfessorDaveExplains]

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

[@manjupatil4717]

Nice intro

[@g02balitakarylleleonec.34]

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

[@alyzaacierto5868]

factors of 3x2

[@mudalad1215]

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

[@brenazelda224]

Ty ^v^ again

[@brenazelda224]

for explains to me

[@kristoffer1085]

thank you math jesus

[@AldreineMAlpas]

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

[@mudalad1215]

its a negative 5 bro

[@jurisenpaiikun1042]

thanks math jesus

[@samuelcrisolo6080]

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

[@ignacioleikis1784]

Is it cheating if I use a graphing calculator?

[@carultch]

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

[@ajprincessderek6229]

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

[@mosyotark1748]

oh no 4:54

[@kaileybump4298]

I wish you were my professor lol

[@senzuicodm6901]

thank you polynomial jesus

[@hackdog1258]

Long hair Beard Helping people Jesus is that you?

[@nerinedesu]

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

[@mmooonnoor6502]

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

[@bigbootybraxyn9801]

😃

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Thanks Jesus

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[@AlessandroZir]

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[@darrenvinculado4293]

I can't understand a single thing

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what the fuck im failing tomorrow

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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]

This is a math tutorial, sweetie.

[@Teiwaz111]

@@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 👍

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Math Jesus

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People don't "wear" hair, bud.

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@@ProfessorDaveExplains 👏👏