How to Sketch Cubic Graphs : ExamSolutions Maths Revision

Here we learn how to sketch graphs of cubic functions which are composed of linear factors and repeated factors.
Go to www.examsolutio... for the index, playlists and more maths videos on cubic graphs and other maths topics.
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[@hadirahimi2794]

Not gonna lie but this is so much better than any other channels I have used to revise. Thank you so much!

[@ExamSolutions_Maths]

Thank you for your comment.

[@7arun9211]

Exactly

[@krishsen6415]

My god, you are amazing ,you explain with fluency and allow me to actually take it step by step. You make everything so simple. Thankyou!👍

[@ExamSolutions_Maths]

Thank you. I am pleased to hear it helped.

[@amirpenkar947]

Thank you very much sir, you have literally explained it better than my teacher and saved me from my stress

[@nuzayerov]

This was so helpful. Thanks a lot. Easy language, clear drawings and easy explanations. I thank you A LOT!

[@ExamSolutions_Maths]

2x+1=0 leads to 2x= -1 which leads to x= -1/2

[@del7920]

This is the best channel for help with math questions. Any difficult math question that I have had, I could find nobody else that could teach as well as you guys. Thank you very, very much. You guys are awesome!

[@ExamSolutions_Maths]

It's just one guy. Me. www.examsolutions.net/about-me/

[@barbie5405]

Ive been trying to find a helpful video and this one is just what i need its straightforward and easy to understand. Thank you so much

[@RaviJAIN_ravi]

excellent ! May i ask you what apps did you use to make this video. Looks very neat, cool and simple.

[@reneeharshita9023]

Underated channel. U deserve more subs

[@ExamSolutions_Maths]

Thanks please share the channel 🙏

[@yoosufnaail2499]

Wow This really helps. Really I mean you are way better than my teacher. Way better. Please make more videos on different topics. I love these. Thank you so much.

[@ramens]

around 10:25 wouldn’t (2-x) make x -2 not 2 since the negative is on the x not on the 2? edit: i checked on desmos and it turns out that i’m wrong, not sure how specifically though

[@ramens]

If it was (x-2) then x would be a 2.

[@andrewombun-tt9fv]

Thank you very much the video really helped me in my study for my math test❤❤❤

[@rabiasharjeel2020]

I WISH YOU HAVE CREATED THESE VIDEOS WHEN I WAS IN MY COLLEGE! SO MANY SLEEPLESS NIGHTS I HAD!

[@mateuszkasprzak4687]

Definitely the best explanation I have heard so far

[@MikeTDOg-wn8vg]

yo I use your website a lot , I'm currently doing AS Maths - are you going to do d1 section , Im guessing it will be hard to do but would be massively appreciated. Also how do you actually do all of this.

[@ExamSolutions_Maths]

+Mike T. DOg I doubt whether I will be doing d1 for a while. How do i do all of this? Put in 10 years of work so far.

[@MikeTDOg-wn8vg]

Okay that's cool , i meant what program do you use to do all of these videos

[@MarvelAnimations]

thank you so much for this, for some reason I've always struggled with this but thanks to you I find this unbelievably easy :D

[@ExamSolutions_Maths]

Cool

[@זאבגלברד]

You can also look at the 6 different cases of a parabulla and the x axis. For each case you can tell how the integral function will look. You conclude that if f(x)=ax^3 + .... then if a is positive then f will be either increasing or increasing-decreasing-increasing. If a is negative then f is decreasing or decreasing-increasing-decreasing. If it has two or three zeroes then it is clear how it looks like.

[@davidhill8163]

great video.. you explained what I needed to know about common mistakes in plotting these graphs. Many thanks.

[@inokajayarathna2670]

You are the best online teacher

[@stellagabriella9085]

this is asmr math i love this channel

[@annihuang4104]

Thank you so much, this was extremely helpful!

[@BTSARMY-uo9ji]

well done and i have learnt a lot

[@mantosh56]

THANK YOU SO MUCH THIS VID WAS REALLY HELPFUL!!!

[@AlessandroZir]

very useful, very clear; many thanks!

[@far8796]

awesome work! really nice

[@heavyhitman]

Great!

[@tamarao.7197]

I didn't understand the turning points. But this video really helped. Thanks.

[@multicolour5879]

This is fantastic help. but one thing I don't understand is how high are the peaks? as i see no units along the y-axis, or is this irrelevant?

[@filmbyben2]

+multi colour in the exam they dont care how high the peaks are for graphs in C1, its only in c2 when you learn about maximum points

[@quack6523]

watched this the day before my exam and got a 97%, thank u

[@ExamSolutions_Maths]

Well done.

[@vardan9307]

Helped me in physics..Thanks

[@spojha01]

Nice explanation sir. Thank you so much.

[@sonyatirmzey7130]

you saved my life thanks

[@ExamSolutions_Maths]

Lord Voldemort Cool. Another life saved. Thanks for using.

[@xingwei7193]

god bless this man

[@redder02]

Great Explanation sir

[@ardaciftci1416]

Wow. You explained it better than my teacher.

[@zainabhassan8349]

Thanks a lot, it helped me understand.

[@davidgoodman8469]

I get this I just cant draw that well I often make the mistake you mention not because I misunderstand the concept but just because i cannot draw would this be something that can cost marks? any solution if so?

[@ExamSolutions_Maths]

You must always show the general shape of the curve, often where it crosses the x and y-axis. If it is not totally smooth don't worry to much.

[@fatinsyukry7190]

thank you sir!!!!😭😭

[@squirrel42069]

Thank you sir

[@stevedl3150]

At about 05:20 you say that the curve will peak at "round about the mid point of x=-3 and x=1...But not exactly the mid point." Why not the mid point ?

[@ExamSolutions_Maths]

Because it is not symmetrical.

[@saltymf_6735]

How can u tell if the graph is negative or positive

[@alfieperkins8138]

Man you are great

[@johnwilson7038]

Very helpful. Thank you!

[@slowcb7310]

no its not

[@georgeacres4]

At 9:09 when you are doing the graph of y=x(4-x)(2+x), I get how you worked out the x coordinatesd at where it crosses the x axis. However, I don't get how you worked out that the y coordinate wherre it crossed the y axis was 0. In the previous one, y=(x-2)(x+3)(x-1), you multiplied the numbers in the three brackets tow ork out the y intercept, which was -2*3*-1=6. In this case of y=x(4-x)(2+x) though, where x is on its own to the left of the two brackets, there is no number there, just x. How do you work out the y coordinate in this case? The second bracket and third bracket numbers multiplied would give 4*2=8, but what do you multiply 8 by to get the y intercept? If you imagine the x on its own to be in a bracket, you just have (x) and no number to multiply by 8 in order to get the y intercept? Essentially, I get that you multiply the numbers in the three brackets to get the y intercept value. When there are only two brackets, and an "x" outside of those two brackets, how do you work out the y intercept? I have multiplied the 4 and 2 in the brackets to get 8, but how do I work out the y intercept when Ionly have two brackets with numbers in? Do you just assume that when there is a solo x and no number outside the brackets, that there is a 0 there, so you multiply the three brackets to get 0*4*2 which gives the y intercept value of 0 that you got? Thanks, I am really confused on this.

[@ExamSolutions_Maths]

You let x=0 for the y-intercept.

[@MissyTheRock]

Heh. 😂 I long paragraph comment for a sentence reply 😂

[@simphiweasah8502]

What about the y-coordinates of the TPs?

[@ExamSolutions_Maths]

This was not the point in this video. If you did want the turning points then do dy/dx = 0 and solve for x and y.

[@simphiweasah8502]

@@ExamSolutions_Maths thank you, sir!

[@semhar4748]

thank you this video was helpful

[@ExamSolutions_Maths]

No problem. pleased it helped and thanks for watching.

[@jamesduffy09]

I was expecting differentiation to be used. What is this tutorial for? GCSE?

[@ExamSolutions_Maths]

James Duffy This was designed for AS students

[@jamesduffy09]

I just did the pure mathematics part of my GCSE further maths today. I would have loved it if the questions were basic like this

[@jamesduffy09]

I appreciate the reply, though

[@rh.5304]

You are AMAZING!!!!

[@kwokblog5460]

On the last example, isn't it a minus x^3 graph rather than a positive, and doesn't past through 4 rather than -4

[@ExamSolutions_Maths]

The graph is correct. When x=0, y=(-1)(-2)^2 = (-1)(4) = -4

[@abdihogsade47]

+ExamSolutions I don't get the x outside the brackets

[@費小笑]

thank you very very very much~♡you saved me

[@fastmushroom902]

nice video

[@Lordknight13]

But I have a question,I cant simply understand how to identify the the highes/mid-point.Due to mid-point I cant simply sketch the graph exact but closer to that.

[@ExamSolutions_Maths]

The highest point does not occur at the mid-point of the intersections with the x-axis.

[@manpreetsinghkhokhar3827]

nice explanation

[@multicolour5879]

Thanks very much, Ben Sasson

[@techforever1970]

Okay, you sir, deserve an award. Where's the donate link?

[@ExamSolutions_Maths]

+techforever1970 Thank you if you do. It's on my website www.examsolutions.net/maths-aid.php

[@daniyals248]

I don't understand why 'x = -1/2' with '2x+1'. Is it because if you divided 1 by 2 you would get a half? (I'm a yr9 student btw)

[@daniel30000i]

because it's 2x+1=0 so 2x=-1

[@olivermincher834]

Thanks

[@rundalshaer4909]

Thanks alot

[@ExamSolutions_Maths]

Thank you for watching.

[@教主蓝教-n9w]

Pardon, i think you have to find the maximum point and minimum point as well......

[@surferbrahhh4547]

i'M SORRY FOR HURTING YOUR FEELINGS. iT WAS A MISTAKE AND i DEEPLY APOLOGIZE SO FOGRGIVE ME!

[@divyde_]

i hope he accepts the apology

[@surferbrahhh4547]

@@divyde_ mE TOOOOOO

[@surferbrahhh4547]

HELLLO HELLO Hello

[@dej69]

1.5x speed makes this so much better

[@ExamSolutions_Maths]

A fast learner you are

[@bengper8044]

What about x^3 -12x+1=y?

[@WipedNBA]

Factorise it first

[@chetafari3035]

Isn't -1 x -4 equaled to 4? I'm confused.

[@gameryl3900]

-1 times -4 is 4.

[@gameryl3900]

Which question are you asking about?

[@jenius8533]

Legend

[@ShanikkaGwyne]

i love u

[@ExamSolutions_Maths]

Pleasure

[@zuccawang4306]

Cool accent bro

[@abhishekpandey9049]

Is it just me.,or he speaks like Zayn Malik.😂 by the way great video

[@landsofqueens4403]

He sounds like big the cat without psychedelics or a british big the cat

[@headshotkiayt9404]

i did all of it but i got the last one wong

[@ceosajid]

wtf -1 x -2^2 is postive 4 not -4 im so losttttt ???

[@nag8649]

Yo, where's the passion?

[@SomEbodyisDERP]

Issokay this is not that exciting anyways

[@dennybuka969]

Why do sound like Prince William???😂😂😂

[@hurera2000]

You sound like Richmond from IT crowd

[@CAL1MBO]

Not at all!

[@peterchen497]

why's ur voice so slow, jarring

[@ExamSolutions_Maths]

I wish I knew myself. Perhaps you would be better off looking at other videos out there that are also free but please thank the guy instead for the time and effort they put in when you find it or not make a comment at all.

[@lorenzycodo697]

this was so helpful thank you so much

[@Hoinam_lau]

thx a lot

[@ExamSolutions_Maths]

🙂