Graphing a quadratic with multiple transformations

👉 Learn how to graph quadratic equations in vertex form. A quadratic equation is an equation of the form y = ax^2 + bx + c, where a, b and c are constants. The graph of a quadratic equation is in the shape of a parabola which can either face up or down (if x is squared in the equation) or face left or right (if y is squared).
To graph a quadratic equation, we need to know some essential parts of the graph including the vertex and the transformations. The vertex of a parabola is the turning point of the parabola. It is the point on the parabola at which the curve changes from increasing to decreasing or vice-versa. The transformation can be a vertical/horizontal shift, a stretch/compression or a refection.
Given a quadratic equation in the vertex form i.e. y = a(x - h)^2 + k, the vertex of the parabola formed by the equation is given by (h, k). Knowing the vertex of the graph and the parent graph, we can then apply the required transformation to obtain the required graph.
'h' in the vertex signifies the number of units left or right the the graph of the quadratic equation is shifted. 'k' in the vertex signifies the number of units up or down the the graph of the quadratic equation is shifted.
Timestamps:
0:00 Intro
2:00 Start of Problem
Corrections:
3:37 I mistakenly said the wrong answer: -27 plus 4 is -23 not -21
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Organized Videos:
✅How to graph a Quadratic in Vertex Form
• How to graph a Quadrat...
✅Identify the Vertex of a Quadratic
• Identify the Vertex of...
✅Complete the Square then Graph | Hard
• Complete the Square th...
✅Complete the Square then Graph | Easy
• Complete the Square th...
✅Graph a Quadratic in Vertex Form with Vertical Shift Only
• Graph a Quadratic in V...
✅Graph a Quadratic in Vertex Form with Stretch and Compression
• Graph a Quadratic in V...
✅Graph a Quadratic in Vertex Form with Horizontal Shift Only
• Graph a Quadratic in V...
✅Graph a Quadratic in Vertex Form | Learn about
• Graph a Quadratic in V...
✅Graph a Quadratic in Vertex Form with Horizontal and Vertical Shifts
• Graph a Quadratic in V...
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👨‍👩‍👧‍👧 About Me: I make short, to-the-point online math tutorials. I struggled with math growing up and have been able to use those experiences to help students improve in math through practical applications and tips. Find more here: www.freemathvideos.com/about-me/
#Graphquadratics #quadratics #brianmclogan

[@wuznab5109]

Something about sitting in a desk with 30+ people and a teacher shoving stuff in your mind, just doesn’t work. But somehow being on your bed drinking some star bucks watching a 10 minute video works.

[@brianmclogan]

haha love it

[@arnavkaul6867]

Holy man I wish I had a teacher like you, so calm and breaks everything down so simply

[@alexfarmer1113]

Couldn’t have stayed it better!

[@angrjones]

@@alexfarmer1113 same!

[@deadaccount2589]

you explained something in seconds that my teacher couldn't make me understand after explaining it 50 times. I'm definitely going to be using your videos from now on.

[@brianmclogan]

awesome! happy to be able to help you out!

[@b.r.u.hb.r.u.h5360]

You just didn’t listen lol

[@jacobgordyn]

@@b.r.u.hb.r.u.h5360 you're on this video because you didn't either lmao

[@becasartori4186]

After three weeks of going through this module I was finally able to learn and understand the day before my test. You saved my grade.

[@Joel-rtn]

I have my Algebra 1 EOC in 2 hours, you've literally taught me how to understand parabolas in 30 mins. We've been studying this for 2 months and mt teacher still hasn't been able to explain it properly, the other day she told us out of 40 of her students, 11 are failing. I'd kill to have a teacher as good as you, thank you for everything you've taught us

[@thatrecord5313]

This teacher is far better than my teacher today! Thank you very much!

[@brianmclogan]

you are very welcome!

[@kelvinle9087]

I think u wrong because -27+4=-23 but u said -21:))

[@brianmclogan]

+Khoa Le thank you for letting me know

[@elyanasweety6525]

Yeah you’re right because -27 +4 =-23

[@zekiseid8965]

I was so confused..like what the heck where did he gt that -21 🤭🤭

[@ritabos7162]

Why the condescending ass tone? relax yourself

[@amiliarek7521]

@Jerry White sameeee

[@readyaimfire3454]

It's funny cause my teacher explained this all to me like 3 times, but I took in nothing. Somehow watching this video in the comfort of my room helped me absorb every detail lol. Thanks so much!

[@Karen-tt3dt]

just learned what was taught in 20 minutes in only 5 minutes! Thank You!!

[@randomroze9699]

You just saved my life! My teacher was so chaotic while teaching us this and I was lost the entire time. Thank you so much!👍

[@jakeschuberg4705]

sheesh

[@MikeMike-yc8gg]

Love your videos , I've always sucked at mathematics and having teachers who over complicate things doesn't help , man your such a blessing...and further prove that with an awesome and patient teacher. ANYBODY can learn ANYTHING .Thank you for being such an essential part of my Journey of Conquering Mathematics!

[@sinzsuperior9841]

After being confuses for a whole week, I watched this video and realised that this was so easy. Now i just need to memorize the transformations

[@haydeeholliday8866]

The explanation of -3 was spot on, thanks!!!

[@brianmclogan]

Happy to help Haydee

[@cindymunera]

Very useful! Thank you so much! I love your channel and I use it frequently. Thumbs up!

[@ella7177]

thank you so much for this video! i was seriously struggling to understand how reflections, shrinks, and stretches worked but you explained it in such a perfectly simple way! i feel like i did really well on my test.

[@CarsynKoenig]

You are such a good teacher I’m going to start watching your lessons before my teacher teaches me

[@kathleenfuchik3779]

You’re a literal angle on earth. Thank you for making math so easy

[@Danny-of3sz]

I got lost at the end lol, but this is the video I was looking for so I will keep rewatching. Thanks!!

[@brucejohnson5786]

thank you for teaching me your ways

[@josh9425]

thank you very helpful ❤️

[@erickavirgile7809]

Thank you, it was very very helpful, hope that you are continuing to teach.

[@kristinnormanton7634]

I'm from a completely different country and my teacher could never explain this to me as well as you have !!!

[@aurun5011]

Unicorn Normy your from the us he’s from Canada

[@suziemarietoller5845]

Unicorn Normy That’s because math’s a universal language

[@zairii9393]

Is it possible to graph a cubic function with just two points? Those points being only an x intercept and y intercept? I'm using the equation f(x)=a(x-h)^3+(x-h)^2+k but it's not working out no matter how I do it. My tutor just plugged in random numbers into a calculator, but I have to explain how I got those numbers. :/ I don't just need the answer, I need the why.

[@cheekscheeks6202]

Thank you , your helping millions of people across the world .

[@YourBoySuli]

Thanksss soo muchh! I was goiing to have a test the next day and I had no idea how to do this because my teacher explained it so poorly, now I understand it! Thanks! Life saverr!

[@VsroYT]

I LOVE YOU SO MUCH I got that q on the test but we have till tomorrow to fix it

[@berserk1864]

Спасибо, всё очень понятно хоть я не так хорошо знаю английский

[@ismaeltp388]

What would happen with our graphic if we delete the first "-3"??

[@dbjmk8083]

If someone asks you to describe the transformation how would you word what happens to the a value at -3?

[@Rose-lz2et]

horizontal shift to the left by 3 units

[@ROYALSPELLS]

I couldn’t understand it when we were learning it during class and I was worried because we had a quiz soon. Thank you so much for explaining it clearly it really helped me finally understand it!

[@brianmclogan]

you are very welcome! happy to be able to help you out!

[@will45812]

I have a quiz tommorow and I couldn't understand it too.

[@serinityschell7240]

Does it matter what point we put into the equation ??

[@augustayarteh7524]

Aw. Brave explanation professor

[@ImBurb]

10 years later but still super helpful.

[@trevorgoodman41]

10 years late, but this information still rings true, thank you for the guidance!

[@dennissanchez5171]

This is great, thank you so much!

[@nicoledasilva3128]

thank you so much!

[@brianmclogan]

you are very welcome Nicole!

[@jakelevine2802]

My teacher sucks so literally these videos are life savers 👍👍

[@overwatchnoob8540]

thanks

[@rubberbund4443]

How did he get the vertex?

[@taejin2648]

Why only times 3?

[@confidential8371]

This guy just did what my teacher couldn’t do.

[@brianmclogan]

🙌🙌🙌

[@rakanalkhalifa9551]

@@brianmclogan u made a mistake it should be -23 not -21

[@batyrn]

This explanation is somewhat axiomatic, i.e. not entirely self-contained. Upon reflection, it's pretty clear why '-3' as a multiplier makes the graph downward sloping and why the vertex is at x=-3 (with y=4). Once the set up is clarified and the drivers are identified this lecture comes together and becomes easy to comprehend.

[@Endersent_]

wut

[@BOWLDEMON]

I just heard him say fuck it

[@maryamalhumaidi]

For which grade this lesson is?

[@urmomcantcook]

10th - 11th grade its alegabra 2

[@azrielsshadowsinger]

do you always substitute x = 0? or can it be any number

[@durga2244]

pretty sure it has to be 0

[@herminiotorneajr.7294]

equation of parabola example y^2=1/2(x=5)^2 answer how to get the y=a(x+h)^2+k?????

[@brianmclogan]

that is not an equation of a parabola, but a hyperbola

[@drugsforhugs7106]

This guy is the Chuck Liddell of mathematics.

[@apanaglima]

7:12

[@RandomThings-ut6or]

i wish u were my math teacher

[@cheekscheeks6202]

We have a teacher calm like him at Morgan Park

[@trishpaytas2773]

how do i still not understand.... i have a small brain i stg

[@urmomcantcook]

i was with him until the y intercept part lmao, i got lost after that

[@mariniecatibog1218]

How to graph y=3(x-3)²+1 and y=3(x+3)²-1

[@stewartkalles9521]

Hey professor isn't negative 27+4=-23?

[@kfjfkeofitorhf9520]

27++(--4)==--23

[@chanelhall1504]

I don't get why he went down by 12, where did he get the 3x4 from? Sorry I'm probably just being dumb :)

[@chanelhall1504]

ohhh nvm i figured it out XD

[@kpaulgagnon5956]

Correction: -27+4=-23, NOT -21. But great job teaching

[@mohamedadan5638]

You are a genius I hope people around the world will respect you as a smart math teacher

[@mohamedadan5638]

Like if you agree

[@enriqueviolador3156]

27-4=21 😂 BRAVOOOO

[@amiliarek7521]

Uhhh 3:32. -27+4=-21 whatttt!?😳

[@elise7566]

thats what I thought....

[@kfjfkeofitorhf9520]

--27++4==---23

[@carmelpule8493]

Write it in another form and it will all become very easy. (Y + 8) = 3( X + 4)^2 and look the value of X and Y that would make what is in the brackets equal to zero, hence Y=--8 and X= --4 (Y --5) = (1/2)( X --3)^2 and look the value of X and Y that would make what is in the brackets equal to zero, hence Y= +5 and X= +3

[@sreemanth9995]

-27+4 is not -21

[@torigrant7864]

It was just a simple mistake😊👍

[@shahriyarsafdar6431]

The graph of y = -3 (x+5)^2 +10 is downward but how

[@han.splash9648]

The 3 outside the brackets in negative, which means it is reflected.

[@maulin_ballin5420]

It is negative 23 and not negative 21.

[@gradhd4359]

april 25 2022

[@jakeschuberg4705]

bru be my math teacher, please!

[@LighthouseFilmStudio]

-27+4 in not 21, it's -23

[@bigbungas1132]

-27+4 is -23

[@declave1317]

-23

[@superjalenentertainmentsys1543]

You said the f word 😄

[@brianmclogan]

when?

[@superjalenentertainmentsys1543]

oh never mind you said all good at 0:12 I thought you said f it but I didn't here good so okay

[@Mist_R]

lmao

[@jake405]

I coulda swore he said fuck it too 😂

[@juicewrld822]

*_G_*

[@francishenrico1752]

saitama

[@juicewrld822]

*_h_*

[@dionysusheir4112]

mines profession, not personal. So....fuck it.

[@brianmclogan]

No worrjes

[@monslay5624]

He is going way too fast!

[@zekiseid8965]

People complaining about their teachers 🙄🙄🙄...its not about teachers, all teachers are same, but depends on you sometimes people enjoy being alone and study alone

[@francescausechelopez521]

BRIAN TE AMO I LOVE YU PLEASE BE MY TEACHER MAKE MY BABIES PLEASE

[@mokeballs6676]

-27+4=-21???