ʕ•ᴥ•ʔ Find the Equation of a Parabola from a Graph with an Easy Walkthrough
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- Опубликовано: 6 сен 2024
- Quickly master how to find the quadratic functions for given parabolas. Watch more lessons like this and try our practice at www.studypug.c...
In the last lesson, we learned how to draw a parabola from its function. This lesson, we will do the opposite. We will learn how to find the quadratic function when we are given the graph of a parabola.
Here we are given a parabola with the vertex at negative 1 and 4. Vertex. The question explicitly tells us the information for the vertex, that means we should use the vertex form to model this parabola, right. Makes sense? Yeah. So let's use the vertex form to model this parabola. Okay? Let's go. So vertex form goes something like this, right, with y on the left side of the equation, x on the right side of the equation with the square right here meaning we are dealing with a quadratic function, right, cool. And the a here is the leading coefficient for the parabola, okay? Cool. Now, vertex. So this vertex information should be able to tell us the information about something here, and something here, right? So let's go. For this vertex the x coordinate is negative 1. So if you want to make the statement look something like this, with a bracket and the x inside, we are looking for a value here, right? Would you say that means we have to move the number to the same side as x, and we can put a bracket around the statement, right? So let's do this. Now, negative 1 is moved to the other side of the equation, it becomes positive 1, right? And now the rest of the equation we just have zero, and now we can put a bracket around this whole thing. And that is gonna be the information we are gonna put down here, right, yeah. So inside the bracket what do we see? X plus 1. So inside the bracket, we just put down x plus 1. And that's done, okay? So the x portion is done. Now let's take care of the y portion. So for the vertex, the y coordinate is 4. Let's do the same thing, move the number to the same side as y. So positive 4 moved to the other side becomes negative 4, and this side of the equation we just have zero. And now, we can put a bracket around this, right. And now we can put this whole thing right here. So inside the bracket we have y minus 4. Inside the bracket we have y minus 4. And now this portion of the equation is done. So now how do you determine the value for the leading coefficient? Well there's still one information we haven't used, so chances are this will help us find a leading coefficient: the information about this point. So let's go. What does this point tell us? What information can we get out of this point? Well, this point is basically telling us that for this quadratic function, when x equals negative 3, the corresponding y value is 12. And guess what? These other values will plug into the equation to find the leading coefficient. Okay? So here, x value, we're going to plug in negative 3. Here, the y value, we're gonna plug in 12. Okay guys? And let's try to solve for a. So left side of the equation we have 12 minus 4, we get-- let me use another color. So, left side of the equation we have 12 minus 4 we get 8 .equals, a is the value we are trying to find. Now, this side we have negative 3 plus 1, we have negative 2. And don't forget outside we gotta have a square, right. Cool. Now, a equals negative 2 squared. Guys, negative 2 squared we get positive, right. Positive of what, 2 squared is 4. So we have 4a. Okay guys. Now, to solve the value for a, to solve the value for a, we simply divide both sides of the equation by 4. That way 4, 4 cancels out. So at the end, a equals 8 divided by 4 is 2. That's it, that's the value for a right here. Okay, guys? So at the end, for this parabola, the quadratic function is right here, okay? Left side of the equation we have y minus 4 equals. . . Guys, what's the value for a right here? A is 2, right? So a is 2. So we put it in right here. Now bracket, inside the bracket we have x plus 1.
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This dude kinda acts like we are complete idiots and THATS why he teaches so well ! Keep it up man, love the enthusiasm
What u said is true
I'm actually an idiot
@@sryifmyenglishsucks792 me 2 when it comes 2 math lol
That is how I need to be taught 😂
I think guys you are not dumb because normally idiots are lazy but you took the time to search this that is good enough
I like how he assumes that we don’t know much, it’s more beneficial than you think!
Yes! Talk to me like I'm an idiot! (Which I kind of am)
@@urkindacyoot47 right. teachers just be assuming everyone knows everything that comes out of their mouth
@@urkindacyoot47 haha
@@urkindacyoot47 cause we are... so i could get it... cause maths is its own language
I wish my instructor was like you. You just showed me what 5 pages of my textbook couldn't.
Haha, really?
@@ne_univayte_pazani True story, read every single page - A'ced 1010 though
Carlos Vega
Hi do you know what smart board they use
true! haha! Have a great day and God bless! :D
@@DNAatWork14 amazing how you're replying after four years woah!
I got two things to say. First, he makes us look like idiots, but two, i actually can understand this shit now. so thx mate
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Yea he kinda does but I rlly appreciate it tho.
If you aren't an idiot there are idiots like me
Yet my dumbass still doesn’t get it😂
You have the kind of demeanor that students gravitate to. Awesome ENERGY!
Thank you! Your feedback powers us up too. :)
Love the energy of this guy
sameeeee
Dijkstra i
I really like the way this guy teaches
He shows the little steps
And doesn't take them for granted. EASY TO FOLLOW.
wow this guy teaches math way better than my 70 year old math teacher.
Thank you! Glad we helped. :)
my teahcer tried plugging in a hdmi cable into his phone truly epic moment
teacher*
@@zjn3898 💀💀
My math teacher never smiled like that
;)
Saaammeeee mine is always pissed off for some reason, he always looks like he doesn't give a fuk and teachs some uni level shit😂😂😂😂
Mine looks like a pedo
@@SirDelu mine is actually one of my greatest friends
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Him: " YEAAAAAA.."
Me: ok.
“YEAAAAAAAA”
literally learned more in 8 minutes from a random youtube guy then my teacher can teach in an hour and a half lecture
THIS!!!!! i went to SIU and he killed every tutor n instructor i had there
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he deserves it ,
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Thank you!!! We will keep trying our best to make math easy! :)
I’ve been scouring the entire Internet for a week to find someone who could successfully teach me quadratics and this is the only video series that has been clear, focused, communicative, and not putting me to sleep. I’m so relieved I found this guy. Instant subscription. Thanks a ton! 🙌🏾🎁
If you’re given the roots instead you can use the formula y=a(x-root1)(x-root2)
For example, let’s say you’re given a parabola with the roots (where the line hits the x-axis) are x=-1 and x=3
Take the above formula, and plug in the roots where it says root1 and root2
y=a(x+1)(x-3)
You flip the signs for the same reason he explained in this video; x=-1 👉🏼 x+1=0
You then take another point on the graph and plug in the x and y values. Let’s say this other point is (0,3)
3=a(0+1)(0-3) *Yes, you will be plugging in the same x value twice.
You then solve, and come up with:
-1=a
Now that you know a=-1, it’s time to plug it into the original equation.
y=-1(x+1)(x-3) *You will leave the roots in the equation. Do not add the x and y values of the other point you used prior. That was just in order to solve for a.
This is in factored form. If you want in standard form all you have to do is distribute, which I’ll show below just for the sake of it.
y=-1(x+1)(x-3)
y=-1(x^2 - 2x - 3) *You have to distribute what’s in both of the parenthesis first. x times x, x times -3, then 1 times x, and one times -3. Combine like terms.
Standard form: y=-x^2 + 2x + 3
Hope this helped. OH WAIT...
If it only has one root, just plug in the root two times. Then it’s the same process.
OK I’m done now.
How can a parabola only have one root? Because it has to intercept the x-axis at some point right? i‘m very bad at math.
And are we allowed to choose any point on the parabola when solving the a? Or the vertex? Sorry for asking so many questions
@@sirinxoxo8031 you probably already figured this out already but im gonna point this out since it bugs me not to. The parabola's vertex (the minimum or maximum) will hit the origin (0,0)
That's when the parabola is considered to have one root.
Y'all so smart tho 😅
EXPLAIN BETTER THAN MY TEACHER
thanks ! glad you liked it .
u da man.
He explains better than all teachers
Him: YEAAAAAA
You know, I wouldn't be so insulted if what you said weren't true. You have to admit even when you don't like to learn from your own video lessons. Do know what just I learned as a "Math Teacher" from these comments? To my classes - "So.... you didn't get it the first time I LECTURED it? Well then... here's a video of an Asian MAN explaining it!" (I'm a SouthEast Asian woman - here's an existential question: Do men or women math teachers get better results?)
I am so grateful for your teaching abilities. My college professor couldn't teach this to me the 2 days that she taught it. I learned it with you in 7mins. You are AWESOME!!!!
Glad we helped! :)
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What I couldn’t learn in 1 year in math class I learned it in an 8:22 minute video 💀. Buddy working some magic here🤸🏽♀️
He is such a great teacher, I fully understand this. Time to ace my quiz :)
Thanks! Good luck with your quiz!
How did you do?
@@divine592 two years late buddy
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i love how he teaches like you don't know anything, cuz when you dont teach me like i was born yesterday, especially when it is something this new to me, it goes right over my head, thx so much dude!!!
Honestly 😂 i understand shit but this guy made me get understanding
The way he talks and explains this makes math so much more enjoyable. I actually learned something!
Now, how come college professors are unable to explain parabolas like this gentleman in the video?
Thank you! Glad we helped.
Because they're professors and he is a study pug
college
Bruh what fucking college are you at. Im learning this in fucking highschool
@@DarthRevan905 dude way more complicated parobolas
I have a test later today I had no idea how to to get a but now I do
We hope the test went well!
StudyPug it did! There was no question like this on the group test but it was on the individual test and this helped a lot! Thanks!
I've never seen a teacher anything like him- his voice is the gentlest tone I've ever heard throughout my years of existence
So, in 8 minutes and 22 seconds, I've learned more in that amount of time than what my teacher has been explaining to my class for a week now. Incredible how something can be taught if the presenter actually knows what they're doing and can explain it properly, assume we know nothing, that's the best way to go about teaching subjects like math in my opinion.
i don’t usually comment on videos , let alone a math video , but this man was really good at this and huge props to him because he’s so positive and helpful . thank youuuu
Thank you very much! Glad you it helpful. :)
Thank you, this dummy actually learned some valuable information. Now I hope I pass the test!
Did you pass?
Gabriella Jaramillo nah
Gabriella Jaramillo already in nursing school:)
@@shantelj7502 you need to learn about parabolas in nursing school???
Fell in love with the concept, not understood in High School
I've been crying and trying to understand how to find the formula for 2 hours. This really helps a lot, thank you so much!
2:27 he has so much energy he is actually jumping to the next part of the problem
The only way to learn math. Rock on!
It teaches me the simple thing that my teacher never teach and know what it totally help me to understand the whole thing. Glad I found this :)
I LOVE THE WAY HE TEACHES. HE MAKES IT SEEM SO EASY.
When teacher assume that we know half the class tends to fail. This guys is the best teach as if we don't know anything .. Wish others will learn from him. Big up yourself Mr
12 years finishing school and haven't understood it very well (in the end im just remembering the formula rather than actually understanding it), here you're explaining it in 8 minutes then boom. Everything went easily and crystal clear, man thank you so much. You litterally helped me out to understand basic things like this for my calculus class
My friend and I are literally struggling so hard right now and you helped so much thank you!
@Rowley_Jeffdeez We're so glad we could help you with Math! Thank you for your message ☺☺
This man has taught me half a unit hours before an assignment on it was due. Thank you, sir!
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@princebrooker9553 He really strives for giving the best approachable method for students to grasp math concepts. We're thrilled to know you find our service helpful.
Thank you for your message! ☺☺☺
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I like how the whole comment section is like "he explains it like we're idiots" but I am one so this helped a lot
I love you tysm I have an online quiz in five min for this
same
I have a hard time paying attention in class and understanding the teacher even when I'm concentrating so this helps a lot
thanks man, you really saved my life, because I have an exam about quadratic functions in 2 days and I knew NOTHING, but now I do :D
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From the very beginning of this video, when you showed the amount of energy you did, I could not stop watching and I instantly got how to do the problem! The way you explained the problem so well was fantastic and I am so happy to have come across your channel, thank you so much for the video and keep up the great work!
This guy teaches as much in 8 minutes as it would take a year for my teacher
Algebra exam in 20 minutes, thank you for teaching me about vertex form quicker than my professor did.
We're delighted to know we could help you out with your Algebra exam! Keep this level of dedication and you'll reach all of your academic goals.
Thank you for your comment 🙂
My textbooks have never failed me like this, and to find this video is a blessing
Excellent. When it comes to maths the ordinary joe is lost. This great teacher has not come to teach you the smart asses but he has come to to teach those who struggle with these abstract concepts. After all everyone has to start somewhere. Well done to this wonderful teacher.
My teacher and this guy are good at teaching but the difference is the way he teaches is the thing that i understand this
YES. THANK YOU SO MUCH!! I hate when ppl teach like we already know or are supposed to know. This is amazing & just saved my life lol I wish more tutors/teachers were like this
We're delighted you liked our video!
Thank you for your comment 🙂
I've never understood math before as clearly as I understood this video thank you
HE TEACHES SO GOOD SO CLEAR..
Got a test tomorrow and I couldn't remember a thing about parabolas but I think this just saved me
This man is an absolute legend. I wish he was my teacher. Keep up the great work studypug.
Thank you so much man, I have my first ever exam tomorrow morning and if I didn't watch this video, I would literally fail. Thanks :)
I could never understand parabolas but the way you teach helped a ton, thanks alot.
@Epico 7 We're glad we could help you out with math! Thank you for your comment 😄
When I show up to math all my teacher says is to open our textbooks and start working for the entire period. I have a test today and I know nothing, you seriously saved me
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This teacher in 8 minutes taught what my teacher couldn't in 1 hour
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@Zahraa A.j Thank you for sharing with us! Feel free to watch all of his free videos here in our channel or absolutely all of his videos in our website. Let us know if you have any questions ☺
i like how im being spoon fed information I LOVE IT I UNDERSTAND SO MUCH
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Oh my gosh I might actually pass my math exam now. I love you so much!
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This helped me alot, I needed visual queues to make the math make sense to me. Thank you you very much.
for those of you who want to save time
(y-f)=a(x-u)^2 where f and u are the points of vertex,
and x and y are the given points, a is the number to be found after doing intense math by plugging values
then at the end plug the obtained value of a and unplug the values of x and y
you talk the exact same way my math teacher does when she's clearly given up on me. good job for emulating that
literally dude if jason mandoza became super smart, it's this guy
This guy is a life saver I have exams in a few days and ik nothing
Taking the psat next week, and my teacher hasn't even explained this yet. So thank you for teaching me this you're a great teacher!!!
DONT EVER STOP MAKING VIDEOS. WE LOVE YA
Thank you!!! We have new videos up constantly. Stay tuned. :)
The energy in this guy is great
dude u helped me Ace my math test thanks man i subbed
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the last 8 minutes was more helpful than the last week before that.
I love this video so much I am in 8th grade AP and was a bit behind, but you really set me ahead. Again, Thank you. :)
You make me love maths for the first time....You are a Legend!!!
You’re a born teacher sir! Bravo! I wish I had you in my math classes!
@ChefGuy49 We'll make sure he gets your comment!
Thank you for your feedback ☺
the way you talk looks like your are directly talking to us which look pretty amazing .none the matter the fact ur not seeing us .
Thank you so much!!! I've been searching for days to find the leading coefficient and you've given me the answer the first 5 min!! Thanks
You taught me more that my math teacher did in a year in just 8 minutes and 22 seconds
@noahborton1568 Is that Trent Alexander Arnold? Liverpool and England Midfielder in your profile pic!
Yes @@ChiragSonne
This is so much clearer than textbooks, thank you
learn more in an eight minute video than in a double class, keep it up man
Although seems a bit cringy, the way he talks actually keeps you focused making it a great lesson. Keep it up ;)
Thanks to this guy for making me pass math class
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This guy should be earning millions!!! Great teacher
Thank you! Glad you liked the video. :)
One question though, in filling the vertex form. You said that the formula its (y )=a(x )² . So in your example you showed that in the edge of the parabola is -1,4 and the upper part is -3,12 . What if it was a different parabola its the opposite of the one you've shown. Which point's are we going to use to fill the formula. This is the second video that I've seen in your channel and I'm enjoying every single part of it and its well explained. I hope I can get a response back. You guys got a new sub keep the math vids up.
In order to make use of the vertex form, as long as the parabola is vertical - either opening up or down, you always plug in the x-and y-values of the vertex.
Thanks for subscribing!!!
@@StudyPug What if you are not given a vertex but only two other points?
Love your videos, subbed for life.
now, he is an AWSOME teacher.