How to find the directrix, focus and vertex of a parabola
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- Learn how to graph a vertical parabola. A parabola is the shape of the graph of a quadratic equation. A parabola is said to be vertical if it opens up or opens down. A vertical parabola results from a quadratic equation in which the x part of the equation is squared.
To sketch the graph of a parabola, we first identify the vertex, the focus and the directrix. To do this, we first write the equation in the form (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus.
After expressing the equation in the form (x - h)^2 = 4p(y - k), the vertex is given by (h, k), the focus is given by (h, k + p) and the directrix is given by the line y = k - p. After obtaining the vertex, the focus and the directrix, we can then sketch the parabola.
#conicsections #parabolaconicsections
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Thanks!
You are welcome!!
happy this video worked for you! some of my videos I get very detailed some of them I shorted everything up. Depends on the class and the day so I am glad you found exactly what you were looking for. I have more examples too just search 10.2 or look for the playlist
Mr. McLogan's Math Channel This seriously saved my butt. I've struggled with my Precalculus homework for who knows how long, but this put an end to it. I was taught so vaguely about these concepts, so when I had to do my homework, I felt like I was being thrown to the wolves. (>.
lol same
u make problems so easy
Brian McLogan kuddos sir😘😘
@KoolGuy this topic is for either calculus and algebra man
Had not looked at parabolas in 25yrs. Quickly refreshed and was able to help my daughter solve her homework. Thanks!!!
you are very welcome! happy to help
I was happy to hear your student at the end say "Ohh" and really understand the concept behind the directrix and focus.
great feeling!
It was a magic moment.
Chris Manhoff thank for the video
thank you very much! I have all my conic sections in playlists or labeled for chapter 10. Let me know if you can't find any particular videos you are looking for
ahhhh sorry I did not bring home my computer last night to respond. I hope you found some of my videos useful and did well on your test. Let me know if I can help you further. I have a couple videos on this information. Just search my videos under 10.2
I love the fact that your students are questioning you if they don't understand something here in my country when you try to tell a point you get kicked out of the room.
I think it is very helpful when learning to create dialogue and I encourage my students to speak up if something does not make sense
Brian McLogan A perfect example of basic communication :) Thank you and Good luck!
I'm stuck doing Pre-Calc on line. You save me, sir. Thank you. I learn more with your videos than I do with my online lessons for sure. Thanks for explaining things!
+Rhiannon Hall you are very welcome! happy to be able to assist you!
thank you so much. I was sitting there with absolutely no clue what to do. I like how you show every step. My teacher doesn't do that and you gave the formulas for the vertex focus and directrix which i didnt have and had no clue how to find because of that.
I wish all math teachers can be like you!!! Very straightforward. I actually understand more now than my hour and a half pre cal class.
happy to be there for you and help you out
wow this video was so informative. Thank you so much, I needed to review conic sections for my calc 2 class... this was life saver!
The way you explain things is very impressive
I learn much more from you than at school
But i want to know where the 4 In the basic formula of the parabola comes from
🙏
Very clear, great video and great teacher
I finally understand this! Thank you for being very clear and straightforward, it was really helpful for me.
awesome! happy to be able to assist you with everything
your videos help me so much thank you
I don't know why but in our university we don't use these methods, which are alot easier and understandable. Thank you very much Dr. Brian.
you are very welcome!
Thank you! You just saved me from my test tomorrow!
happy to help, you are very welcome!
these videos are saving my math grade :)
Thanks a lot . This video help me so much for my final exam!!
Augusta August Happy to help, how do you think you did?
I think I can get perfect score ;)
Thanks for the quick maths
Thank you very much sir :) this is much better than our one hour class :3
happy to help
Helped me quite a bit- thanks
SHDmusic you are very welcome! happy to be able to help
saved me once again..What a legend..
YOURE THE GOAT
Thanks a lot. I have learnt so much from this. 😊
except how to spell
savage
This is really well explained,thank you
***** happy to be able to help you out, let me know if there is anything else I can do for you
Do you have a lesson on horizontal parabola's I have this equation that I have to find the focus for: x= -1/8x^2. Not sure how to find the focus.
The lockdown brought me here.
This channel is my savior
Amazing.. Thank you. God bless
This helped me a lot, thx!
+Nate Walls you are very welcome! happy to be able to help you out
Subscribed to your channel tnx for this free tutorial
you are very welcome! happy to help!
are you in
Does the 4p represent the slope of the parabola? And if somehow you remove the 4p from the equation, can you derive the vertex form of the quadratic equation?
+speedlearner 4p is the same as "a" in vertex form y=a(x-h)^2+k it does affect the compression and stretching of the parabola, we do not use slope because parabola's do not have a consistent slope between points.
+Mr. McLogan's Math Channel I knew I was on the right path. The reason I referenced the slope intercept formula was that x - h looked similar to x2 - x1. I figured that if you subtracted k from both sides of the quadratic function vertex form equation, y - k would look similar to y2 - y1.
The only thing I don't comprehend now is why x - h is squared. Could you explain this to me?
OMG Thank You soooooo muchhhhh!!! you explained this soooo clearly !
+Sayra Rodriguez you are very welcome! happy to be able to help
could u please give an example of writing a "standard" form equation into vertex form by completing the square/
10.2 How to find the focus of a parabola given an equation in this video you said to find the focus is (h,k-p) but on this video you said is (h,k+p) which one is right?
The value of p is negative so therefor h-(-p) is the same as h+p
Thank you so much
Let me just say being homeschooled is really hard to do math but I came across your videos and now math is becoming sooooo easy for me. Thank you so much you're now my teacher and I your student :))))
absolutely! let me know if there is anything else I can do to help you
I have a test tomorrow and I don't know how to quite do when they ask "use the information provided to write the vertex form equation of each parabola"
Examples: Focus:(-1,6), Directrix:y=2
Vertex:(1,-2) Directrix:x=-7 Like I don't even know how to start doing it... help!
Thank You sooooo much!!!!!!!!
Thank you for your videos. Much appreciated. Can I ask what is the second fomular you said in the video and use it for what case? Thanks again.
I am not sure I remember what I was referring to.
Thank you! So much for this video 🏅😂💆🏻 you explained it well
appreciate it, happy to help
how would you do this for a horizontal parabola set at the origin (1,1)??
imacatmeowmeow1 same process
My teacher literally doesn't teach. . . but you certainly do :)
really helpful videos thank you!
Love your vids man , haha wish you could take my tests for me 😂
happy to help
This was fantastic
you just saved my brain from self-destruction :D
haha been there before!
:D
Thanks a lot ! That really helped
very helpful
thank you
thank you for such a great video!
you are very welcome! happy to help
I have a big problem. What if there is a number in front of the y?
say
4y = x^2 - 12x + 52 how do you find the vertices and focus?
I got completing the square I just don't know what to do with the 4 in front of the y
you have to divide that 4 in front of the y on both sides before completing the square
how about the Axis of symmetry?
btw thanks!!
good luck, let me know how you do
i have a test tomorrow, it's 12:05 am from where im from and i need to wake up at 4:30 am. and here i am binging on sir Brian Mclogan XD
you got this Nyrem! best of luck
so helpful better than my teacher
happy to be able to help!
I'm studying for a test and the equations sheet that I'll be given says that the equation of a parabola is (y - k) = 4p(x - h)^2. I'm confused since the equation used in this video is not the same: (x - h)^2 = 4p(y - k). Can someone help me with this? Am I overthinking this?
I believe your formula sheet is incorrect the 4p should be on the linear term not the quadratic
Thank you for getting back to me and clearing up my confusion! Knowing that 4p should be multiplied by the linear term will help me to remember the correct formula.
Are all smart teachers kinda bold or is it just in my school?
what if the given is (x+2)^2=-16(y-3)???
is this correct?
vertex: (h,k)
focus: (h, k-(-16))
directrix: x= k+a 👉 x=k + 4
latus rectum: 4am 👉 -16
sorry I am focusing on preparing for my next school year your vertex is (-2,3) focus is 4 away where 4p=16 so p is 4
can you do trigonometry functions grade 11
I have a ton of trigonometry videos, just search my channel for what you are looking for
proud of myself that i dont have any questions to ask :D
bam!
i kind of confused me can you try and simplfly it a little bit please
tieler gray sure what part is most confusing to you or what are you having trouble understanding?
Why do I feel like I wanna clap.
still finding the answer to my homework.😥
still?
Brian McLogan Yess. its very complicated the problem is -vertex at the origin,Focus:(0,-1/32) they want me to find the vertex form of that.😥What am i suppose to do?😥 please help me Sir Brian.😔
the distance from the vertex to the focus is p which in this case is -1/32. Since the vertex is at the origin (h,k) is (0,0) Since you know the value of p, h and k, just plug them into the formula, since the focus is below the vertex you will use the equation for a vertical opening parabola
school is so unnecessary
Just give this guy an oscars!
happy to help!
i guess your a good teacher in math
where did you leave
You explain things better than my teacher does in a 2 and a half hour lecture!
SAME
thank you
you are very welcome!
He looks so much like Randy Orton.
+Anindividual I'll take it
Can you post more videos on how to find the directrix, focus and vertex of a parabola? I have a couple different problems but they don't look like that. Thank you! I love your channel!
You saved me just in time for my Precalc final!!! Thank you so much! You are an awesome teacher!
you are very welcome! best of luck
Do you have a video on how to find the equation if given the focus/vertex or vertex/directrix ?
This could quite possibly be the most explicit explanation of such a convoluted subject. After watching your video, I was able to determine where I was making mistakes in determining the values of "p", and thus finding the focus of the parabola.
THANK YOU!
Joshua Impson perfect! so happy to be able to help you out!
As a result of your video, I was able to nearly ace a quiz this week. KUDOS!
Hey man 4 years late and i learned more in 11 minutes then what my math “teacher” tried to teach in 2 weeks
: ) happy to help!
yes that formula is when the vertex is at the origin
I missed class this day and I have a quiz tomorrow. You just saved my grade!
haha love that movie, been there done that, happy to help!
i just learned more than what my teacher has thought me in 4 class periods
awesome! happy to help as always
Who else’s teacher sucks at teaching
Yes there are many different ways to represent conics. I prefer this method. I like Dr. Brian wish I could go back and earn that name.
Literally you saved me my teacher makes no sense you’re amazing thank you
this more easy to understand than the one hour class
glad to hear
+Mr. McLogan's Math Channel sir how should I get the r1 and r2 of the latus rectum?
sir can you please tell me how we can find out the focus point if we have only aperture length, aperture width and aperture area only
It's helpful that the students are in this because I had some of the same questions!! So helpful.
you will then have to complete the square so it is in vertex form : (
If the focus of a positive parabola is (h,k-p) is the focus of a negative parabola (h,k+p) ?
you would need to write it in vertex form by competing the square
Thank you for your videos. Much appreciated
Thank u!!
what we were to find was like this but horizontal aos.. this became my guide, super thankful for this vid!
you are very welcome!
thank you so much for your videos!
i am from México and i can learn english and math at the same time!
regards! :)
de nada
you are welcome!
you are very welcome!
you are very welcome!
So in my NCEES Handbook it has the equation set to: (x-h)^2 = 2p(y-k)....why does this give me 2p but the equation you spend time on say 4p?
You are a godsend, so many videos on youtube don't provide the examples I need. The always convenient ones and are not the current problems I am dealing with.