How to find the directrix, focus and vertex of a parabola

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!

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You are welcome!!

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I learned more in these 11 minutes then in my 2 hour long class

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+makeusaywa t that's why I love teaching on youtube

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+makeusaywa t lol same thank you Mr. McLogan!!

[@guadsquad7775]

mine was 3 hours and right after a test. Its awesome that these videos are still helping people 4 years later.

[@markjosephpm4226]

A big help indeed haha 3 hrs of class vs. 11 minutes of video and I can see the difference.

[@victoriamoreno4966]

same

[@renewd]

I was happy to hear your student at the end say "Ohh" and really understand the concept behind the directrix and focus.

[@brianmclogan]

great feeling!

[@renewd]

It was a magic moment.

[@nanasarpong1829]

Chris Manhoff thank for the video

[@brianmclogan]

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

[@mooremik]

Had not looked at parabolas in 25yrs. Quickly refreshed and was able to help my daughter solve her homework. Thanks!!!

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you are very welcome! happy to help

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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.

[@brianmclogan]

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

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Brian McLogan A perfect example of basic communication :) Thank you and Good luck!

[@RosaLopez-cw8me]

You explain things better than my teacher does in a 2 and a half hour lecture!

[@nonyabizness577]

SAME

[@brianmclogan]

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

[@faithnozomi7031]

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. (>.

[@shubhamkatyal6391]

lol same

[@nareshvichare1480]

u make problems so easy

[@jadesingga]

Brian McLogan kuddos sir😘😘

[@angielapaulino4791]

@KoolGuy this topic is for either calculus and algebra man

[@brianmclogan]

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

[@joshuaimpson2553]

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!

[@brianmclogan]

Joshua Impson perfect! so happy to be able to help you out!

[@joshuaimpson2553]

As a result of your video, I was able to nearly ace a quiz this week. KUDOS!

[@theluckybarbarian]

Hey man 4 years late and i learned more in 11 minutes then what my math “teacher” tried to teach in 2 weeks

[@kielygudino1958]

You saved me just in time for my Precalc final!!! Thank you so much! You are an awesome teacher!

[@brianmclogan]

you are very welcome! best of luck

[@maxwelleckenrode4676]

It’s funny that I never get the help I need from most of the KZbin videos I come across. Until all of a sudden I always find one of your videos and everything is cleared up to me in less than 10 minutes. It’s also awesome that your students ask enough questions so that almost nothing is left out and can clear up any misunderstandings we might’ve have beforehand.

[@brianmclogan]

soo happy to hear my videos have helped you out Maxwell

[@KevinNguyen-zx2px]

Do you have a video on how to find the equation if given the focus/vertex or vertex/directrix ?

[@brycenhaugarth1780]

Just wanted to say please never stop doing what your doing, you have helped me so much. Thank you.

[@adamjuwaied8068]

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!

[@hayleynymphadora1216]

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!

[@brianmclogan]

+Rhiannon Hall you are very welcome! happy to be able to assist you!

[@mcmoy214]

It's helpful that the students are in this because I had some of the same questions!! So helpful.

[@rm-09]

Honestly, thank you so much. Our Math professor is atrocious in his teachings, and his lectures are what nightmares are made of. You made this topic extremely simple and easy to understand. Thank you, again!

[@karenfrancis5202]

I tutor and find your videos more helpful than the teacher notes that the students provide. You clearly know your material.

[@BiscuitVillain]

Gotta say: all of your videos have been SAVING me since I'm doing online class. I swear this is the worst way to learn lol But you are great! Thank you for the easy to understand explanations!

[@hippybecca]

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.

[@prashantsaini6372]

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

[@emilyirizarryrodriguez2148]

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!

[@diegotheexplorer4210]

Oh, now I get it. I was wondering about the connection between the focus, directrix and vertex. Thank you!

[@TOYCH]

Thank you for your videos. Much appreciated

[@kenjiro2676]

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.

[@spiceaddict1118]

You just saved my life. Thank you so much for going through step by step

[@stacystacy754]

He looks so much like Randy Orton.

[@brianmclogan]

+Anindividual I'll take it

[@JoelyY]

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.

[@brianmclogan]

happy to be there for you and help you out

[@haleyperry420]

Literally you saved me my teacher makes no sense you’re amazing thank you

[@rere9290]

i think i've learned better from this video than the hour and a half long math class i've been going to 3 times a week for the past couple of weeks

[@brianmclogan]

+Hugh Jass great to hear and happy to help you out! keep up the hard work

[@tassmo328]

If the focus of a positive parabola is (h,k-p) is the focus of a negative parabola (h,k+p) ?

[@PuffoPufferfish]

Is the directrix always "y = k - p", or is it "x = k - p" on a horizontal line of symmetry parabola (left/right opening)

[@jwoodsonmusic]

I missed class this day and I have a quiz tomorrow. You just saved my grade!

[@clintx123]

thanks Dr. Brian, i have some question so what could be the Latus Rectum of that(the problem in the video) ? is it 4(1/2) so the answer would be [LR = 2] and so 1 unit from the left 1 unit to the right of the focus. Right?

[@brianmclogan]

awesome! happy to help as always

[@laurapoelstra2981]

I finally understand this! Thank you for being very clear and straightforward, it was really helpful for me.

[@brianmclogan]

awesome! happy to be able to assist you with everything

[@tesfafuture648]

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 🙏

[@UnivisionProduction]

Thank you! You just saved me from my test tomorrow!

[@makaylahoward9240]

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.

[@jacobzu6655]

You are so patient and descriptive! In a college precalculus course right now and you're helping me out a ton. Entering Calculus this summer :-)

[@brianmclogan]

good for you, keep up the hard work! I am teaching Calculus this year so hopefully I will have many more lessons that can help. Just let me know if there is anything else I can do

[@brianmclogan]

happy to help, you are very welcome!

[@baonganhoang2068]

Thank you, I have a lot of trouble to understand my professor and you make everything so much easier.

[@brianmclogan]

Very happy to help you out Ngan!

[@dylanwerelius7550]

Thank You so much. I'm in Honors Alg 2 and this is how I understand things better.

[@bigpackage8513]

Very clear, great video and great teacher

[@nuevosarahjoyt.8525]

You're so great sir! Thankyouu for this kind of video❣️

[@JJRivRiv]

helped loads on studying for my final. thanks for taking the time to record and upload this !

[@brianmclogan]

you are very welcome happy to help!

[@njorogekiratu2427]

Amazing.. Thank you. God bless

[@lenasalim166]

these videos are saving my math grade :)

[@AriaFamily]

Hello professor Would u please explain the wide graph and narrow graph I’d confused

[@pmarkpmark]

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?

[@brianmclogan]

haha love that movie, been there done that, happy to help!

[@brianmclogan]

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.

[@gregl2249]

could u please give an example of writing a "standard" form equation into vertex form by completing the square/

[@MrSalehovich]

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.

[@brianmclogan]

you are very welcome!

[@duchades8609]

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.

[@brianmclogan]

I am not sure I remember what I was referring to.

[@MadmansKnowledge]

How would you find the directrix and focus if you are given an equation in quadratic or "standard" form?

[@anthonygillespie9640]

Brian you are goated my guy

[@tashasolorzano8545]

thanks so much!!!! i fell asleep in class today!!!! the teacher sounds like that guy from the movie "bueler's day off"!!! lol! i wish i had you as a teacher!!!!

[@brianmclogan]

: ) happy to help!

[@tumadre9689]

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 :))))

[@brianmclogan]

absolutely! let me know if there is anything else I can do to help you

[@AssyrianKing4ever]

if the vertex is at (0,0), cant we just use the formula x^2=4py? if not when do we use this formula?

[@jhunmichaelibanez2362]

Wow. A video made 8 years ago helps me today.

[@brianmclogan]

you would need to write it in vertex form by competing the square

[@Afromonkey1998]

Thanks for the quick maths

[@narissax]

can anyone tell me how he was able to know the vertex by looking at the equation

[@brianmclogan]

you are welcome!

[@luciatao9579]

really helpful videos thank you!

[@minykick]

thanks lot, we went over this in class and I have this all written down but for some reason it just didn't click, it is making much more sense now. Time to finish my homework

[@brianmclogan]

awesome! go and get it!

[@hansikag1]

thank you so much this helped me for my EOC tomorrow. thank you!!

[@brianmclogan]

best of luck!

[@amandaarenas4345]

This was extremely helpful!! great for midnight cram sessions lol

[@brianmclogan]

happy to be able to help

[@imacatmeowmeow1]

how would you do this for a horizontal parabola set at the origin (1,1)??

[@brianmclogan]

imacatmeowmeow1 same process

[@brianmclogan]

yes that formula is when the vertex is at the origin

[@ashleytorres5193]

i just learned more than what my teacher has thought me in 4 class periods

[@Latifawabinthafialbadia]

This is really well explained,thank you

[@brianmclogan]

***** happy to be able to help you out, let me know if there is anything else I can do for you

[@TheKaylizzle]

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!

[@pawanprakash4131]

sir you are awesome.... now i get it clearly....thank you

[@brianmclogan]

happy to help!

[@TrevellGrant]

Big Help... thank you!

[@brianmclogan]

+Trevell Grant you are very welcome!

[@libris3403]

Thanks. You explained it so much clearer than my professor.

[@brianmclogan]

+Samuel Flores happy to help!

[@kristagob4268]

Thank you for this, it helped me a lot right now

[@jonathangillooly9361]

My math class taught this a different way, but this is so much easier! Thank you!

[@brianmclogan]

you are very welcome!

[@oliviahamukwaya6099]

Thank you for your videos sir I have learnt a lot.

[@brianmclogan]

you are very welcome! happy to be there for you!

[@emmay120]

your videos help me so much thank you

[@shaneandres5755]

Thank you very much sir :) this is much better than our one hour class :3

[@brianmclogan]

happy to help

[@flameforce4000]

Thanks a lot ! That really helped

[@harvey6287]

Thank you so much you're a life saver!!!

[@brianmclogan]

You are welcome Tandano

[@eggxecution]

instant subscribed. Keep it going, now I know about parabola!

[@brianmclogan]

awesome! and happy to have you!

[@zechteri]

The lockdown brought me here.

[@anthonyburgers1317]

This channel is my savior

[@rickiemaralit3184]

thank you for this 11 minutes video. HAHAHA it really make sense and it did help me study parabola easier.

[@brianmclogan]

awesome! happy to help

[@renedominguez6430]

thank you so much for your videos! i am from México and i can learn english and math at the same time! regards! :)

[@brianmclogan]

de nada

[@user-fw4jt6po8b]

This is explained in the most complex way

[@JacobVossFilms]

This was fantastic

[@denzilaerlonfloydgodoy510]

Thank you so much! Like I was so confused about this problem lol.

[@brianmclogan]

you are very welcome! happy to be able to help

[@henry5807]

This guy is very helpful.

[@brianmclogan]

happy to help

[@anjann7680]

i'm going to take my calculus exam tomorrow! thank you for this!

[@brianmclogan]

you are very welcome! good luck

[@brandonkelley2989]

Love your vids man , haha wish you could take my tests for me 😂

[@brianmclogan]

happy to help

[@Dyleniz]

Thank you so much I needed to learn this since I'm failing my class and my teacher gave me a chance to catch up with my grades by giving me a make up test

[@brianmclogan]

awesome! happy to be able to help

[@TheThefirstman]

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

[@brianmclogan]

you have to divide that 4 in front of the y on both sides before completing the square

[@Thestarsalign15]

learned so much than spending a week or so on this topic in class and thank you