Graphing Polynomial Functions Using End Behavior, Zeros, and Multiplicities

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.

Related Videos to Help You Succeed!:

End Behavior

Take Your Learning to the Next Level with Me!:

Subscribe to the Channel

Get my Learn Algebra 2 Video Course (Preview 13 free video lessons & learn more)

Learn Algebra 1 Video Course

Looking to raise your math score on the ACT and new SAT?
Check out my Huge ACT Math Video Course and my Huge SAT Math Video Course for sale at

* Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below)

[thelastasolplayerrip]

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

[lovemorembasela]

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

[taopinairlinesmathindustry]

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

[blissbenson]

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

[JayTo]

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

[sejintennant]

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

[ataberdi]

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

[bearmcevers]

I didn't know Jeff Bezos was a math teacher

[JediKnight_Tot]

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

[yourmathtutorvids]

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

[jerrysmith]

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.

[jackiek]

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

[penelopeperez]

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!

[triciakruse]

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

[Kewser-uu]

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

[marryjoynapat]

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 just I'm so grateful, that I can sleep right

[ThaoNguyen-ybxq]

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

[asmaazayan]

You are really fantastic ❤
KEEP IT UP !!!

[emmasnyder]

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

[xiaosongwu]

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.