Advanced Functions 3.3 Characteristics of Polynomial Functions in Factored Form

[@shoheb.i]

Thank you so much for your help! I'm taking Advanced functions next year in grade 12 and I wanted to get some work done early to get a better understanding and you are really saving me with all your help! THANKYOU THANKYOU THANKYOU.

[@mshavrotscanadianuniversit6234]

You are most welcome. And kudos to you for being so proactive! The kind of student I would have wanted in MY class!

[@oblivionfps6058]

The partial factoring and shift on the end helped A LOT!!

[@mshavrotscanadianuniversit6234]

Good to hear! Hope I’m teaching you well! 😊

[@BabaSphere]

I wish KZbin would let us like a video more than once! These are so good thank you so much miss

[@mshavrotscanadianuniversit6234]

You are most welcome! Thanks for supporting the channel by watching and commenting. Please encourage your friends to subscribe to the channel. A mere 34% of viewers actually subscribe 😳

[@somilarora4130]

I got 90 in grade 11 functions So thank you so much and I have advanced functions this semester!!!!!!

[@mshavrotscanadianuniversit6234]

Good for you!! Keep working hard!

[@Kothoi]

Hey there! If you don't mind me asking, what did you get in grade 12 advanced functions? 🤔 I'm just curious to know! 😊

[@mshavrotscanadianuniversit6234]

@user-jr9qi6so1e I loved math and had very good teachers. I don’t have my report cards (I AM old!) but I do know that I was at the top of the class.

[@atramansoury877]

Hi Miss, in the time stamp 10:16: what do order 1 and order 2 mean? I appreciate your videos so much!

[@mshavrotscanadianuniversit6234]

Order 1 means a single root which passes through the x axis and order 2 means a double root which means the graph will only touch the x axis and then go the other way. 😊Thanks for asking and watching.

[@atramansoury877]

@@mshavrotscanadianuniversit6234 I got it, thank you miss!!

[@ghazal.g8318]

Thank you, life saver at 1:30am

[@mshavrotscanadianuniversit6234]

Stop procrastinating! 😂

[@tejaljariwala419]

oh god not me here at 4am trying to complete 3 lessons before class starts hahaha

[@tns_lover9271]

Thank you for the video :) Your videos helped me prepare for the course

[@Jacobismaelthethird]

Why couldn't you factor (x2+2x-2) in the last example you shown to get the actual zeros? Example J I think

[@mshavrotscanadianuniversit6234]

That equation is not factorable but you could approximate the zeros using the quadratic formula 😊

[@atramansoury877]

I love this video it makes math so much fun and understandable. I have a question for 19:16. Wouldn't it be -4 +8?

[@atramansoury877]

When I put the whole thing into my calculator I get 12, but I dont get it because 2 to the exponent of 2 equals 4, and -4 x 1= -4, and -4 x -2 = 8. So all together 4 + (-4) + 8 = 8. Can you tell me where I went wrong

[@mshavrotscanadianuniversit6234]

⁠​⁠​⁠ Oh goodness! I know exactly what you did and it’s not an uncommon mistake! You did an expansion of the terms which gave you that extra term. You don’t multiply the -4 x 1 AND -4 x 2 For example -4(1)(-2) does not equal (-4)(1)+(-4)(-2) It equals (-4)(1)(-2) It’s all multiplication 😊

[@atramansoury877]

@@mshavrotscanadianuniversit6234 Ohh I got it miss awesome thank you!!

[@moski9861]

Hello Mrs.Havrot's. I am currently in grade 12 advanced functions learning Polynomial functions in class, and so far you have helped me understand better than my own teacher. But I have one question, I don't understand how you found the order. Both for odd and even functions. How do you find the order?

[@mshavrotscanadianuniversit6234]

So if it says a function has a root of order three you would know that it has a triple root.

[@moski9861]

@@mshavrotscanadianuniversit6234 what exactly does a single root, double root and triple root mean? does it mean one zero, two zeroes and three zeroes ?

[@mshavrotscanadianuniversit6234]

No, watch the very beginning of the video where I explain how it all works on a graph

[@reading-_____-5299]

Thank you so much for the help!! I have a quick question, how did the textbook sketch the graphs for number 9, since the given equations are in standard form? For 9 a) I factored out and got the zeros, but I am a bit stuck for the remaining questions. Thank you for your time, and consideration.

[@mshavrotscanadianuniversit6234]

These questions all involve factoring; some by grouping and common factoring and factoring or trinomials. Here is a step by step solution for b - d mshavrot.pbworks.com/w/file/fetch/145546236/3.3%209%20b-d.pdf make sure to check out some of my notes on PBWorks

[@reading-_____-5299]

@@mshavrotscanadianuniversit6234 THANK YOU SO MUCH!! YOU ARE LITERALLY ONE OF THE BEST MENTORS!!!

[@sukyzheng3136]

Hi Ms Havrot! When we say that there is a "double root" or "triple root" does that mean that the graph touches the x-axis two times/three times as in having two/three roots? but most of the time when i graph them the places where there are double or triple roots it only shows one x-intercept?

[@mshavrotscanadianuniversit6234]

Sorry, my computer was in for repair! Yes, a double root means something like this f(x) = (x-2)(x-2) so in effect you have two roots of 2, which shows as touching the axis in one place. Similarly for f(x) = x^3 you actually have a triple root at x = 0 or you could think of it as f(x) = (x)(x)(x) three roots of 0.

[@sukyzheng3136]

@@mshavrotscanadianuniversit6234 ohhhh ok that makes so much more sense!!! I guess the double/triple root concept is more useful for graphing then :))

[@gm_esm03]

Omg this was the most helpful thing I’ve seen. Thank you!!

[@mshavrotscanadianuniversit6234]

So nice to read your comment! Hope I can offer a lot more "insights" as you watch the videos. : ) AND don't forget to subscribe!

[@saims.2402]

How does the discriminant tell you how many roots there are? How do you use that? What lesson is that from? Thank you Ms. Havrot.

[@mshavrotscanadianuniversit6234]

Functions 3.6 The zeros of a quadratic function (Discriminant)

[@mshavrotscanadianuniversit6234]

You need to review this lesson from grade 11

[@saims.2402]

@@mshavrotscanadianuniversit6234 thank you so much Ms. Havrot!

[@mshavrotscanadianuniversit6234]

kzbin.info/www/bejne/rnXLhICtd7hngLs

[@malakamer7758]

Hi Mrs. Havrot! At 17:37 you talked about how (x^2+1) is non-real root. How do we identify non-real roots in general (do we just try to solve for them and see if it works?) Thanks!

[@mshavrotscanadianuniversit6234]

Yes that’s correct. Remember from grade ten that if you are trying to solve a quadratic and you have a negative number under the radical (on its own also known as the discriminant) then you don’t have any real roots. Same if you have x^2 = -1 because, once again, you can’t take the square root of a negative number. 😊

[@malakamer7758]

@@mshavrotscanadianuniversit6234 okay i see, thank you :)

[@somilarora4130]

thank you so much for your help!

[@sukyzheng3136]

and also - is the sign of the leading coefficient just the sign of the "a" value in the factored form equation?

[@mshavrotscanadianuniversit6234]

yes, you are correct

[@Gabriel-vk7nt]

can anyone explain why she factored the negative out of b but not c

[@mshavrot_math]

I’m not sure at what point in the video you are talking about but I’ll guess you mean b) and c) around the 6 minute mark? If so you must remember that you only factor out a negative that is in front of the variable (x in this case)

[@farmaansingh8248]

thank you so much ms

[@mshavrotscanadianuniversit6234]

You’re welcome! Thanks for watching. Be sure to share my channel and get others to watch and subscribe.

[@EEEE-zs8sz]

Can anyone explain the order thing?

[@mshavrotscanadianuniversit6234]

Watch at 7:54 on this video. Order one means the graph of the function passes through the x axis. Order two means double root or you could also say that it only touches the x axis at that point.

[@EEEE-zs8sz]

​@@mshavrotscanadianuniversit6234 thanks for the reply, what if the order was higher, like 3 or 4, what would it indicate in that case

[@mshavrotscanadianuniversit6234]

Three is a triple root (think y = x^3) Four is a quadruple root (like y=x^4) You wouldn’t have anything higher than that to deal with.

[@EEEE-zs8sz]

@mshavrotscanadianuniversit6234 Thanks! Helped a lot as i have a test next thursday and really needed this.

[@mshavrotscanadianuniversit6234]

@EEEE-zs8sz Good luck! (Although luck will have nothing to do with it!)

[@unozaddy1445]

you're the goat

[@mshavrotscanadianuniversit6234]

Thanks! 😊