ʕ•ᴥ•ʔ Quadratic Functions - Explained, Simplified and Made Easy
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- Опубликовано: 28 окт 2015
- Quickly master how to find characteristics of quadratic functions. Watch more lessons like this and try our practice at www.studypug.com/algebra-help...
Three properties that are universal to all quadratic functions: 1) The graph of a quadratic function is always a parabola that either opens upward or downward (end behavior); 2) The domain of a quadratic function is all real numbers; and 3) The vertex is the lowest point when the parabola opens upwards; while the vertex is the highest point when the parabola opens downward.
Let's learn some vocabulary for quadratic functions. First, vertex. What is a vertex of a quadratic function? Well, the word vertex means peak. So the vertex of a quadratic function is the peak point on a parabola. Which means for a parabola opening down, the vertex is the highest point. Now for a parabola opening up, the vertex is the lowest point. So in this case, we have a parabola opening up, so the vertex is the lowest point, right here. Sitting at x equals 1, y equals negative 9. So the vertex is at 1 and negative 9. Next, axis of symmetry. The axis of symmetry of a quadratic function, is a vertical line that divides the parabola into two equal halves, like this. And the axis of symmetry must always pass through the vertex. The symmetry behavior can be best understood when we fold the parabola in half along the axis of symmetry. Then the right half of the parabola will completely overlap the left half of the parabola. Can you see that? Let me show you. Here we have a parabola, just like this one, and the axis of symmetry runs down the middle of a the parabola. Now, I'm going to fold the graph along the axis of symmetry. Can you see that? The two halves of the parabola completely overlap each other. Yeah? Cool. Now let's determine the equation of the axis of symmetry. For a vertical line that passes through x equals 1, the equation of the line is simply x equals 1. Because for every point on this vertical line, the x coordinate is always 1. So in this case, the equation of the axis of symmetry is x equals 1. Next, y intercept. The y intercept is the point where the parabola intersects the y axis. So in this case, that's right here and the y intercept is negative 8. Next, x intercepts. The x intercepts are the points where the parabola intersects the x axis. So in this case, the parabola intersects the x axis at two points. One at x equals negative 2 another one at x equals 4. Next, domain. By definition, domain is the set of x values for which a function is defined. So as we can see, a parabola is defined for all x values. Let me show you. This point, the x value is positive 1. This point x value is positive 2. This point x value is positive 3. This point x value is positive 4, and this point x value is positive 5. So a parabola is defined for all positive integers for x. Now if you take any points in between, now see, these points the x values are positive decimal numbers, right? Yeah. So a parabola can take on any positive values for x, whether they are integers or whether they are decimal numbers. Parabola can take on any positive numbers for x. Now, guess what? Parabola can also take on any negative values for x. For example, this point x value is negative 1. This point x value is negative 2. This point x value is negative 3. You see, negative integers. Now, for any point in between them, for any points between the negative integers, this point the x values are all negative decimal numbers. So in conclusion, parabola can take on any positive values for x. Parabola can also take on any negative values for x and parabola can even take on zero for x. That would be this point, for the y intercept, the x value is zero, right? So therefore, the domain for a quadratic function is all real numbers. And we write a mathematical notation like this, x is all real numbers.
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You can tell he enjoys teaching, that positive attitude makes it so much easier to understand, unlike my teacher who has such a monotonous tone that the only challenge is staying awake during her class.
TRUE!! HAHA
IKR i have that same issue!
Sounds like my teacher... mrs. Manly
For some reason I find his accent to be annoying, possibly because I am Chinese myself and I used to have that same accent but I’ve completely gotten rid of it and his accent reminds of a time when I sucked at English. I am in no way trying to insult him I think that he’s a great teacher but I’m just saying that I would like him better if he could speak normally
@@unclewillibomb8683 Well... At least we can understand him.
I always have a really hard time understanding during class because I get distracted easily, but this was simple and straight to the point. Thank you so much, it was extremely helpful.
James Merchant Same!! :")
same dude
Same I would do better if you could rewind what the teacher is teaching
i feel ya, but i don’t get distracted my teachers just crap
Same
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My teacher takes more than 30mins to teach us but I didn't learn anything.
But this guy only did it in 8mins and I learned a lot!😂😂😂
Reasons
- His voice is so good you will never stop listening
- Too many distractions like your crush
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@@joseantonioperez5989 all fax
Right!!
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Mine always makes my class guilty that we don't know concepts that we never learned 😭 You're so right tho!
Who is here to study for a test?
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Gamer Kev me bro
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Here for an IGCSE exam which is tomorrow
My midterm's tmrw
Time stamps for anyone wondering (and for my own self reference):
0:04 - Vertex
0:59 - Axis of symmetry
2:50 - Y-intercept
3:09 - X-intercepts
3:36 - Domain
6:08 - Range
6:48 - Minimum/maximum value
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I like his accent, it is cool and a bit decent.
It was his accent that made the whole video more interesting.
shawn Malig its a northern chinese acent
@@chloroplast8611 but you can't really hear it..it's wierd
It's like an Asian Bob Ross.. he just sounds so chill
Yeah I like his accent alot
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yea
Me
i am being forced to complete highschool in a month while in 8th grade
I’m still stuck
@@MrSploingus what??
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my teacher's voice is so boring
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StudyPug dude I can never sleep when I'm supposed to and whenever I'm not I feel sleepy...
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MightyNighty7 did what work?
YOU SIR ARE A BLESSING FOR MY 11-GRADER SELF WHO'S HAVING A MATHS EXAM TOMORROW. THANKS SO DAMM MUCH for explaining something I never understood from my maths teacher DAMN
IJustWannaComment NotMyRealChannel 11th grade???? bro i’m in eighth
@@emiliaryan2108 In which goddamn Country you study parabolas in 8th standard? Fukin hell
Tf I study dat shit in 8th grade
gr 9 math 😭
Random dudes,The first time I got to know about parabolas was in 11th Grade! THE educational system in your Countries are pretty cruel! They are killing the child in you in such a tender age. Ok,Bye.
This man just saved my life by teaching me in 8mins what my teacher couldn't teach in 80 and as a plus it was relaxing and enjoyable rather than confusing and panic inducing
i cant focus in online class
This shows how math can be easy and fun. It just depends on the teacher.
@mrpickle499 We're glad you found our video easy and fun.
Thank you for your comment! ☺
I struggled to do graphing for 4 years and this handsome man just taught me how to do it in seven minutes...........Thank you
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Isss so relaxing
Oscar Parent lol
Home unintentional ASMR
and that slight static in the background is actually smooth, not piercing
all hail parabola
All hail cheese
Cheese is E
E for cheese
parabla*
lol
@@souju8755 parabola
*The Smile of Success **7:46** LOL*
XD
Oof
Thank u i was confusion
No problem! Glad you found the video help. :)
I love how he says “parabola”lmao
“prabla” lol, its so cute
I always thought it was para-bola
@@ladykilljoy9864 para-boe-la
He's adorable! after going over every single definition, he turns around and does this little half smile/smirk. It's as if he's looking for approval like a little child...This just makes me love the video even more, as well as help me to understand quadratic functions better. So thank you!
This helped me so much! Tomorrow I am taking my Algebra 1 eoc and I wanted to review so many things in such a small amount of time, i thought it was impossible since I didn't get Algebra at all, until I started checking this channel and reviewing everything. Thanks to this I might even get the chance of getting commended!!! Love this, keep making videos 💯
how'd it go?
how'd it go?
I guess he failed
*dead*🤣🤣🤣🤣
I have mines on May :')
*This was honestly so helpful, plus he seems nice, so its much easier to learn*
Gotta love the smile after every explanation, my teacher has literally just assigned this crap and given us nothing to go off of, thanks for helping still in 2020
same haha
Awwww i love everything about this video,the great vibe he gives off, his smooth talking. The way he explains and how he enjoys teaching
Thank you so much for this video it really helped
This helped so much! I'm slowly understanding Algebra thanks to you 😊
You sir, are an excellent teacher. Clear yet compact. Thank you!
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Who else is here for an online class?
The explanation for this video was done immensely well, and your videos never become vapid. I just have one question on the domain of a parabola, that is the domain always all real numbers for every Parabola, or is just in this video that the Parabola's domain is all real numbers? If there is another answer for the domain of any Parabola, can you give an example?
Vikram Upadhyay The domain is always all real numbers for a Parabola, assuming it is y=ax^2 + bx + c.
If the form of a parabola is in y = ax^2 + bx +c, its domain is always going to be all real numbers. However, if it is in the form of x = ay^2 + by + c (sideways parabola), its range is always all real numbers.
Good Job! You are right. :)
GOSH thank you so much
Basically the domain is the numbers that can be plugged in as x. In this, you can have x be any number and you will find the relative position of y at some point on the parabola. Due to the exponent, a higher x value will be exponentially higher of a y value than, say, 1 less than that x.
you know when your student don't want the lesson to end and is excited about what comes next that's when you know you are the best teacher and you gave me that feeling , thank you.
Gosh, thank you SO much Studypug. The money this channel spends to advertise their channel and website is WORTH IT. Very clear, simple, informative. Also, cheers to the person in the video because he is very enthusiastic about the topic.
This guy talks so softly I'm falling asleep. Very relaxing, kinda sounds like Bruce Lee
Lol. A new great use of our videos - Watch us before you go to bed! *Caution of side effects: A better math mark :)
Hahaha kinda hahahaha
Anyone else 2019??? How am I just finding this?!
i am
I just found this in 2020 ._.
The sounds he make while he writes on the board is SOO satisfying
I can't thank you enough man u rock real life saver greetings from Africa
You're very welcome! Glad we helped. :)
You easily could be the best teacher on earth, your explanations are so god damn clear and easy to follow. Plus, that smile at the end of every explanation is just the cherry on top. :]
Thank you so much! this video really helped me to understand quadratics. Online schooling has made it quite hard to learn things but this is really easy to understand and enjoyable to listen to and watch! subscribed ❤️
hello!!! im a 9th grade student and was really struggling with quadratic functions for a month. my school teacher and home tuitor's explanations didn't stick with me and their teaching style didn't help me at all. I thought I was just dumb until I went on youtube and found videos for the topic, many videos didn't work until I came across yours. Your method for explaining, calm and steady tone and flow really stuck with me. It helped me a lot to study for my finals and I easily followed along. I finally understood the topic 100% and didn't feel there were gaps in my understanding like before. Thank you so much! you're helping so many students so keep doing what you're doing. God bless you :)
i love the noise of his pen tapping on the board its so comforting
i wish this guy was teaching my zoom classes
I had no idea graphs could be so easy. No words
why can't teachers sincerely smile at me like he does??? because it's really encouraging :(
Superb. Top-notch quality explanation. He allows the student to absorb abstract concepts by "taking his time". This a great failing of many other maths teachers, they rush through the concepts and the student is left bewildered. Excellent presentation here.
MY LIFE HAS BEEN SAVED!
everyone needs a teacher like him
This guy is basically the Bob Ross of algebra.
In Vietnam we learn these stuff in grade 8 and early grade 9. Now I study in Canada and completely forget wth is this :( Thanks to your voice i do understand so well
No problem! Feel free to check out our other videos if you ever need more help. :)
I’m Vietnamese too
In California we learn these grade 7 or early 8
@@matcha721 same in Florida but it’s in 7th
You explain things so well! And so enthusiastic - thank you.
This is the kind of attitude I need when I only have 5 classes to study for my test.
We're learning parabola's on Wednesday and the first thing i'd want to know is the vocabulary, THANK YOU U MADE THIS SUPER EASY AND HELPFUL!!!!!!
Now, I finally get it. Thanks!
Bro your explanations are great, keep the good works sir!
i hardly leave comments and i’m not sure if you will even read this, but i just wanted to thank you for the clear and simple explanation. you were able to teach me in under 10 mins something i was so confused about in class. you’re a great teacher thank you so so much!!! i subscribed
I have a test tomorrow and you came in clutch. Wish you were my teacher. Love from east asia, I wish nothing but the best for you and the rest of the team behind the youtube channel
And from the StudyPug team we kindly appreciate your wishes. It takes a great deal of work from many awesome people to carry on this project.
Thank you for your comment 🙂
What program are you using? I love it. You are so easy to understand, great job!
This is wayyyy better than the videos we are assigned to watch 👍 an easy explanation
Yuleidi Carbajal Thanks for your comments! We're always glad to help students with math. Any question or comment we are here to listen!
i have just learned a months of quadratic geometry lessons in 7 min. This best teacher so far. period.
Was not what I was looking for but still saw the whole video because I like how he explains it
watermelon Mendoza same
Love this teaching … such enthusiasm, calm, and confidence. Learning made doable! 👏 Thx!
This video saved my grade, thank you!
I don not know who you are, but what I know is that I wanted that prospective of learning to understand completely a quadratic function. Thank you man, you do a great job
I wish you were my teacher, you just seem so happy and make me wanna listen
Wow, nice explain study pug. I can learn about the graph. Study pug is my favorite mathematics channel.
I am bad english, but i am bright in the mathematics!
Thank you! Glad you like our videos :)
When your studying last minute for a math exam because you couldn’t understand a unit you did 6 months ago...anyone?
man quarantine has completely messed up my learning. my teacher just left us and didnt meet with us at all online last year and boy i had to earn this myself in a workbook.
This guy’s aura makes learning this fun
I absolutely love how well you are at explaining things, this video was extremely helpful and I loved it.
Thank you! Awesome! Glad you liked it.
How do I stop fangirling over him?! 😭❤️❤️
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@@1w598 bro chill
@@1w598 ay wtf
OMG IM SO CONFUSED TO THIS WHEN MY TEACHER IS TEACHING ME THIS! THANKYOU FOR THIS VIDEO!!♡
This is more ASMR than anything else, it's weirdly relaxing. Love his attitude tho you can tell he likes teaching, and he was super easy to understand, his teaching is better than my 20 pages of online school XD.
Hey man what smart board are you using I wanna get my school to buy it for our teachers thank you.
Great video and explanation BTW
Subscribed
sweet! welcome! the smartboard..it's 2d rendering! j/k
why is it that ive learned more math from this 7 minute video then I have from honors math 2 teacher for the past 2 months
Thank you so much I hate algebra and this really helped me understand quadratics
Learning about quadratics now because when I had to learn them in school the teacher ONLY made us use the book and kept me up until 1am doing tedious homework and I didn't remember a thing from her class. This is so much easier. Thanks to actually good teachers who love their jobs, like this guy!
Neolin thank you for your comments! We're so glad we were able to help you! Any question or comment you may have we're always here listening. ☺
I just wanna know what you were writing on , it looks so fun lol
Michelle B probably a smart board
Dumb board
you tech great this has helped me a lot
thank you for your feedback!
THANK YOU SO MUCH!!!!! I have watched MANY videos trying to understand Quadratic Functions and I couldn't understand it till I Watched Your Video
Amazing. Surpurb, fantastic. This is the best teaching I think I have ever seen. We need more teachers like this guy
Thank you!
You're welcome! Check out all of our video lessons at studypug.com :)
How am I suppose to focus on the board when you are looking so cute 😫❤️❤️
His smile after every point made me me happy to learn
Really needed help Understanding this Subject and you taught me Everything I needed to Know in just A couple A minutes!!! I had know idea what my Teacher was teaching me 😂 and now I’ll be prepared for My Test tomorrow. YOUR A LIFE SAVER, THANK YOU!!☺️
He sounds like he is using maths as pick up line when talking to girls
This makes me sleepy lol because of that marker
HOLY MOLY man it takes me so long to find a math video that makes me understand but everything you said I remember thank you
اسطورتيي وربي 😭🔥
your voice is so OMYGAD so relaxing, pls be my teacher! whahahaah
My teacher never does this T^T. She explains it tho but it makes me more confused. Thnx
You're welcome! Glad we helped make it clear to you. :)
Cause your teacher sux, like mine.
you made it so easy to understand, love the enthusiam!
why did I just realized there's a ʕ•ᴥ•ʔ in the title, anyway I found this really relaxing to watch
I wish I were Asian then I would be smart
Does not work lol
oct 2018 anyone?
mee!
December mate
this probably the only thing about algebra i understood thanks to you :)
Finally this is what I'm looking for thanks man I had no mistake in definition of quadratic function
Dad is that you?
\ʕ•0•ʔ/
I want him to be my teacher in Math.
Blaze Gaming I want him to be my bf
i love how this guy just smiles when he does something.I don't know what's going on inside his mind but I think he believes I actually get this.
Tell me where can I get a Math teacher who's as great as him
He made this lesson so direct to the point which makes it much easier to understand
Thank you so much!
Who here just took a poop and felt like studying
Just me ok :(
whaa that is umm a bit weird
WMT_Mickey big fax I did the exact same lol