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

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

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

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

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great feeling!

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It was a magic moment.

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Chris Manhoff thank for the video

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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

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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. (>.

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Brian McLogan kuddos sir😘😘

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@KoolGuy this topic is for either calculus and algebra man

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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

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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.

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

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SAME

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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

[@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!

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

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

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

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

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you are very welcome! best of luck

[@KevinNguyen-zx2px]

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

[@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!

[@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

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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!

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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.

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soo happy to hear my videos have helped you out Maxwell

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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!

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

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Thank you for your videos. Much appreciated

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awesome! happy to help as always

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

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

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

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

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He looks so much like Randy Orton.

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+Anindividual I'll take it

[@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.

[@brianmclogan]

happy to help, you are very welcome!

[@diegotheexplorer4210]

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

[@laurapoelstra2981]

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

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awesome! happy to be able to assist you with everything

[@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

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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.

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: ) happy to help!

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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 :-)

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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

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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.

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

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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.

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happy to be there for you and help you out

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

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

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you are very welcome happy to help!

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Very clear, great video and great teacher

[@tassmo328]

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

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

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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!

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Thanks a lot ! That really helped

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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!

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

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these videos are saving my math grade :)

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really helpful videos thank you!

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This is really well explained,thank you

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

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

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Very happy to help you out Ngan!

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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

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

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Amazing.. Thank you. God bless

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Big Help... thank you!

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

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YOURE THE GOAT

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

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best of luck!

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

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You are welcome Tandano

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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 🙏

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

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Thank u!!

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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.

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

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OMG Thank You soooooo muchhhhh!!! you explained this soooo clearly !

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+Sayra Rodriguez you are very welcome! happy to be able to help

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Thanks for the quick maths

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

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awesome! and happy to have you!

[@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?

[@imacatmeowmeow1]

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

[@brianmclogan]

imacatmeowmeow1 same process

[@PuffoPufferfish]

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

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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!!!!

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absolutely amazing. Helped a lot. keep up the good work.

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thank you will do

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

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happy to be able to help

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Thank You sooooo much!!!!!!!!

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Thanks a lot. I have learnt so much from this. 😊

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except how to spell

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savage

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

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happy to help!

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This guy is very helpful.

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happy to help

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

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

[@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

[@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.

[@brianmclogan]

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

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your videos help me so much thank you

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

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you are very welcome! happy to be able to help

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Thank you so much

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

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de nada

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super helpful; thanks!

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Elizabeth F. you are very welcome! happy to help!

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

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you are very welcome!

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

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happy to help

[@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

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awesome! go and get it!

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Thanks a lot 💚

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you are very welcome!

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This helped me a lot, thx!

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

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

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This was fantastic

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

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happy to help

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

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thank you for such a great video!

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you are very welcome! happy to help

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

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awesome! happy to help

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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.

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omg thank you...i needed to learn this...subrscribed and liked!!

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eddie lopez : ) happy to help!