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
I have a test tomorrow, thank you so much...
@muutrich
3 жыл бұрын
@Latifa Alawadhi this comment was made 9 months ago man, the guy passed the course already lmfao
@ciaraboone
3 жыл бұрын
mine is in an hour 😳
@Sam-fv4xq
3 жыл бұрын
@@ciaraboone mine in 3 hours
@vapecat17yearsago85
3 жыл бұрын
Nah I ALREADY did the test. Teacher wants me to show work so I put this LMFAO
@Aaradhya9797
3 жыл бұрын
@@ciaraboone soo sad...🤣
Thank you for explaining everything better than my teacher lmao
@mesumabbas9481
3 жыл бұрын
Yeah those hearts are only restricted to beauties.
tthank you so much for making this video I really had no idea where to start with these problems
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
thanks professor for making this video.it has further motivated me in loving the algebra
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
3 жыл бұрын
Hii
Hi, nice video. I recommend you also to explain how to plot polynomials of multiple variables. It would be great)
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
2 жыл бұрын
Right sir
@TheTemporaryLasters
Жыл бұрын
it is a hidden quadratic
Hi, what's the solution of the factoring? thanks.
Thank you very much, This is so helpful.
This guy is a big help ❤️
Finally......., I got it ....., Thanks a lot sir😍😍
Hi there, would you like to make a series about Elliptic Curve Cryptography (ECC) in future? I would love to learn from you.
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
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.
Thank you!
Thank you very much professor
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
3 жыл бұрын
Yep
@ha5541
2 жыл бұрын
Yeah
@kexcro8972
2 жыл бұрын
He’s not wrong the x and y axis don’t have to follow the same scale.
@agenericboringhomosapien8108
2 жыл бұрын
Yup...
Thanks for clearing my concepts of this topic Very nice method of teaching
thank you this is exactly what i needed
Very infotmative. Impressive. I'll be subscribing
i understood everything except for the factorization of the comprehension exercise, can someone explain it to me? plz?
I have a test later. Thank you!
Holy shit you explained this so perfectly my math teacher could never
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.
Thank you, sir.
Can someone explain me the comprehension quiz
i see 2 zero does it get multiplied and gives 4?
6:49 KZread’s red line is jumping out
thank you, god of math
this is way better than going to school💕 I literally understand it😎 thanks again 😄
this tutorial is Damn good I think im' get at least check in this part of the quiz tomorrow
@foodisgood7607
3 жыл бұрын
shut up
@doctorbolsen
3 жыл бұрын
@@foodisgood7607 Shut up
you can get the y values by plugging the x'es in the equation.
Thankyou!
YOU ARE THE BEST -from KICS
Superb.
If all math teachers were like him or has his attitude I think many students wont need to watch this type of videos.
Thanks sir
thank u for that saved my time
can someone explain to me how he resolved the comprehension equation? nvm I got it
Thankyou so muchhhh
Thank you, Math Jesus
you just explained everything my math teacher failed to do in a semester lol. thanks
Great explanations But 😄😄 how did you study on your own to understand at such deeper level?!!😁😁😁(aka your study tricks)
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
Ай бұрын
like on the (x+1)(x-1)(x+2)(x-2) because if you plug 0 in you do get +4
thank you, I have an algebra II test tomorrow and you probably saved me a failing grade.
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
2 жыл бұрын
rational roots test, it's covered in my tutorial on synthetic division
@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
11 ай бұрын
Thank you
Ofc Professor Dave has a video on every topic I need to study. (insert a blessing from the lord meme here)
watching while taking the test
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
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
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
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
4 жыл бұрын
Trinity Lugo yea np we’re all here for help
@TheFirstNamelessOne
4 жыл бұрын
The method is factoring bu grouping.
@ict12-3a_aranetarannyb.2
3 жыл бұрын
@@eneu9069 8:30 in this one a same procedure of it? kinda confuse
I have a test later and im gonna clutch it
Uh when i tried to make the zeros in the checking comprehension its (x + 1)(x + 4i)
@mudalad1215
6 ай бұрын
its a negative 5 bro
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
Жыл бұрын
we're dont. thats bc it's just sketch
@shivanshuawasthi2485
Жыл бұрын
it's just a rough idea about the graph of polynomial
I got my mistake made a mistake to consider the zeros to be even multiplicty thanks for the video
Done.
i didnt knew you explain math problems
3:46 How did we get (x+3)(x+1)(x-1)=0?
@alyzaacierto5868
3 жыл бұрын
factors of 3x2
@mudalad1215
6 ай бұрын
3 times 1 times -1 is 3, and -3
thank you math jesus
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.
Nice intro
"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!" 😂😭
Ty ^v^ again
@brenazelda224
Жыл бұрын
for explains to me
Can you explain maxima and minima by using calculus
@ProfessorDaveExplains
5 жыл бұрын
yes i have a tutorial on that! somewhere in the calculus section, has to do with second derivatives
thanks math jesus
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
It doesn't make any sense to me. 😵. Even though, thank you for teaching.
Is it cheating if I use a graphing calculator?
@carultch
Жыл бұрын
Depends on who's asking you to produce a graph of the equation.
I wish you were my professor lol
thank you polynomial jesus
Me writing this comment to come back and tell myself the grade I got
@xama5x.
Ай бұрын
How much u got?
@biggestloseroftheday2598
Ай бұрын
yeah how much did this guy get
@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.
Ай бұрын
@@Asian_Boii congratulations
oh no 4:54
I'm so dumb, i still don't get it...
😃
Long hair Beard Helping people Jesus is that you?
❤️❤️🙏🙌
ياريت تتاكدوا من جواز حكم وضع الموسيقى او الاغاني ع مقاطعكم عشان تتجنبوا الوقوع بالاثم وشكرا لكم ربي يحفظكم
yaann yaannnnn
@ikari3394
3 жыл бұрын
YANYANYAN
@samalexies
3 жыл бұрын
Yanyanyan
@samalexies
3 жыл бұрын
Module pa nga
Thanks Jesus
@tacoexpressSEEDEEholeeveryones
2 жыл бұрын
jeeeehehehehehe an an an an
Math Jesus
what the fuck im failing tomorrow
I can't understand a single thing
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
2 жыл бұрын
This is a math tutorial, sweetie.
@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 👍
men should only wear short hair
@ProfessorDaveExplains
2 жыл бұрын
People don't "wear" hair, bud.
@designingworld6611
2 жыл бұрын
@@ProfessorDaveExplains 👏👏