Finding the standard form of a parabola given vertex and focus

Learn how to write the equation of a parabola given the vertex and the focus. A parabola is the shape of the graph of a quadratic equation. A parabola can open up or down (if x is squared) or open left or right (if y is squared). Recall that the focus and the vertex of a parabola are on the same line of symmetry.
When given the focus and the vertex of a parabola, recall that the focus of a parabola is inside the parabola. This enables us to identify the direction which the required parabola opens. We also need to identify the value of p, which is the distance between the vertex and the focus. p is negative when the parabola opens down or left and is positive when the parabola opens right or up.
Once we identify the direction and the value of p, we can use the equation of parabola given by (y - k)^2 = 4p(x - h) for parabolas that opens up or down and (x - h)^2 = 4p(y - k) for parabolas that opens left or right
#conicsections #parabolaconicsections

[@brianmclogan]

4 Mistakes Students Make with This Parabola - kzbin.info/www/bejne/mYGwZGaHjs6mjc0

[@jimreynolds619]

man, i really wish my teacher was you. my teacher is so confusing and explains things horribly. your 5 minute video explains everything that took my teacher 2 hours. Thank you so much

[@brianmclogan]

happy to help

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[@esharana3818]

Same!!

[@detraviousbrinkley7152]

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[@russellmcculloch8967]

Bro, I learnt how to graph from the standard form in 5 mins from these videos, and my teacher taught over 2 weeks and I didn't learn a thing

[@mfrekejohnson5191]

Mr. Brian, you, you are a true lifesaver. This was so hard for me to grasp in an entire 45-minute class, but with this 5-minute video, I understand this easier than the alphabet. Thank you for all you do.

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Professor McLogan, your videos have been my lifeline throughout this semester! I can honestly attribute my success in the conics portion of my pre-calculus class to you and your fantastic videos. I made the (rather poor) decision to take a 5 credit pre-calculus class through my college's online program where the workload is very heavy, and I have struggled to keep up. Thanks to you, however, I've managed very well these past few weeks. Thank you once again for making such helpful material widely available to those who need it!

[@brianmclogan]

Very happy to be there for you Noah. Congrats on working hard and making the best of your decision. Your hard efforts will pay off.

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Survived my SHS days with you professor and now here i am again for my 1st examination as a college student!!

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[@motheroftwo5551]

Not sure if this will help, but many of you asked about what to do if the focus has a fraction, as my problem does. What he did without really saying it is he took the 4 from the focus and subtracted the 1 from the vertex to get 3. So, for instance if you have vertex (3,5) and focus (3, 79/16), you would do this: 79/16 minus 5/1 and find the least common denominator to get -1/16 as your "p". Once you do this, just slip it into your formula: (x-3) ^2 = 4 (-1/16) (y-5). Of course, you will need to multiply 4/1 and -1/16 to get -1/4. And then just use all your algebra 2 mathematics to solve the problem. Your final answer will be y = -4(x-3)^2 +5. I hope this is not confusing, if so I can give more details.

[@user-fi2ed9oh4n]

Thank you so much!

[@hikigayachan1124]

I understand you than my teacher who teaches thing for 1 HOURRR, thank you for this!!

[@mustafamalik4211]

2nd part of my final exam tomorrow :P Thank you so much for your videos, they're a great method of reviewing

[@brianmclogan]

you are very welcome! best of luck!

[@turkeyman3019]

Oh my goodness. THANK YOU SO MUCH! You made what seemed like hieroglyphics into something I can actually understand.

[@brianmclogan]

Awesome!!

[@cqneeded7950]

just spent a half hour looking for a way to do this, this was the only video that helped,. thanks mate keep it up

[@brianmclogan]

happy to be able to help

[@hawychan7776]

Thank you very much. 💕 from Philippines

[@nalasleafhearts6497]

Thank you so much for all these videos, I was absent when we first went over this and whenever my teacher does these problems he rushes over it and barely explains. Probably because he normally teaches calculus and IAT is very easy to him and were one of the rare years he's teaching IAT instead of all calculus. I really needed this because most of the kids in my class cheat off each other on tests because no one gets it except the kids who have tutors teaching them and I feel extremely guilty when I cheat on tests.thanks again

[@brianmclogan]

you are very welcome! happy to be there for you, I know exactly the feeling of you and your students, been there many times. Let me know if there is anything else I can do to assist you

[@jigsawpuzzle509]

Im new to your subscription 😊 Thanks alot now I know how to find the standard equation 😊... So sir is it the final answer? Or I need to multiply it? Cause mine is X=1/8(x² - 4x +12)

[@esharana3818]

OMG!! You literally have done all the questions that i need help with. Best teacher in the world!!!

[@brianmclogan]

happy to be there for you Esha!

[@khushisingh4192]

Thank you so much sir . You helped me a lot.

[@chinnie18.]

Oh my god thank you sir you save me from my pre calculus subject I love you sir

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[@swapnamoola9465]

very well explained👍

[@TheBacker007]

Amazing explanation.

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I got an 100 on my test because of this video! Thank you so much

[@brianmclogan]

awesome! great work!

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You're the real GOAT

[@sourabhpandey7018]

I am from india . It clears my concept.thnx dear professor

[@11235Johnson]

Thank you for the guide and hopefully I ace my test in a couple of hours.

[@brianmclogan]

hope you do as well, best of luck

[@TheLuischavez6]

Wow this video really helped me for my quiz and now I'm currently studying for my last midterm and final... With that said thank you very much.

[@brianmclogan]

you are very welcome! happy to help you out

[@warriorgaming-bs1234]

I am from INDIA ... I understand your speed English language not properly but it sufficient for understanding this question......😎😎nice teaching method sir

[@davidandmattstump9881]

literally my mind makes sense of this

[@brianmclogan]

been there done that! haha

[@giaannevillagracialaguyo5988]

Brian McLogan I think you forgot to write squared while you were solbing for the perfect swuare trinomial it must X squared minus 4x plus 4

[@amer6522]

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[@brianmclogan]

be careful, I upload a lot! However I do have 90% of my videos organized in playlists so that should help you out for multiple examples

[@drewsimone100]

that thing on your head was distracting me

[@brianmclogan]

it was a boo boo

[@prateeksenapati2152]

Thanks Mr. McLogan. Your explanation was amazing! : )

[@brianmclogan]

you are very welcome! happy to be able to help

[@marfeliz7143]

Another way that can help you figure out which standard equation to use is by remembering that the (x-h)^2=4c(y-k) equation is to look for the number in the coordinate that the vertex and focus both have in common. In this case that number is two, which lies on the X portion of the coordinate. Thereby, I remember that I have to use the (x-h)^2=4c(y-k) formula. If the vertex were at (0,3) and focus (0,-1) then I would find that the 0 is the common number that they both share, which is on the x and write the equation for the origin : X^2=4cy.

[@brianmclogan]

thanks for sharing

[@ashikulislamnabil8062]

Thank for the video..it helps me lot..want video lecture on calculus..

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Sir superb explanation sir well understood

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Thanks man, even though posted 4years ago it's still helping me out

[@brianmclogan]

that is why I love KZbin

[@Faiyam]

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[@brianmclogan]

+MrTrollygames awesome! happy to be able to help!

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Professor youre the best

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omg man thank you im taking a test and you just saved my life though

[@brianmclogan]

sweeet! happy to help, hope you did well!

[@zainabsiddiqui6154]

haha same

[@wafa-ug3bt]

thank you so much i had no idea what i was doing before

[@jackleahyschannel4567]

Thanks for the video it really helped me out! I thought I was gonna do terrible the rest of the year and the regents (The test we take at the end of the year if you didnt know what it was) because in 2 hours of help per day I still never got it but by watching 5 minutes of your videos I get it completely. Also I was wondering was this filmed in front of a live class that your teaching?

[@brianmclogan]

+JackLeahy'sChannel great to hear, and I hope you do really well on your test, yes I record myself actually teaching every day

[@rafaelsoltura1782]

What would u do if its in a fraction form likr the vertex for example is -1,-3 then the focus is -17/16,-3

[@tiasghosh2825]

Tnk u sir ur vedios are amazing. U explained it very easily that my tuition teacher was unable to do.

[@brianmclogan]

happy to be there to help you out!

[@maranablue2148]

what a great help! thank you sir.

[@brianmclogan]

you are very welcome!

[@bensonkings1300]

This is really great.... I have understand, ready for exam now

[@brianmclogan]

awesome! happy to help

[@dragonascent8501]

How do you make an equation if all you get is the focus? For an example the focus is (0, 1/3). How would you solve that?

[@jvst5717]

THANK YOU

[@orangemegamind]

Sir, how do we obtain standard equation form for horizontal parabola which consists of 2 cases present at left or right? And, even what about the vertical one? And how do you

[@adameinum8544]

Thank you! If if you didnt make theese videos i would never graduate.

[@brianmclogan]

happy to be able to support you, your hard work is paying off

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thank you sir ")

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Thank u so much, you saved my life

[@brianmclogan]

Happy to be able to help you out!

[@euli5804]

can I ask why you add 12 on both sides on 4:30, thank you!

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You have a video for everything thank you

[@brianmclogan]

you are very welcome!

[@raniarovich]

I think you switched up the h, k values for both formulas in the comment sections maybe I'm wrong ,can you tell me if I am?

[@jeriesakroush7763]

Hello Mr McLogan, do you have videos on how to find the directix and foci of quadratic parabolas on your yt channel?

[@rBJ817]

Thanks Brian

[@brianmclogan]

you are very welcome!

[@daisy-zz5tn]

THANKS FOR THIS!

[@brianmclogan]

you are very welcome!

[@aroojkhan9110]

so helpful thank you

[@brianmclogan]

you are very welcome!

[@gustavorodriguez8894]

you explain better than my teacher. she just uses the textbook to explain us . thanks for your videos

[@brianmclogan]

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

[@deeswagg4444]

This video is very helpful. I was wondering what equation you would use if the parabola was horizontal?

[@jimreynolds619]

dont know if you still needed help but, you would swap x-h and y-k, so it would be (y-k)=4p(x-h) if its opened to the right, or (y-k)= -4p(x-h) if it is opened to the left

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youre literary godsent

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sir you just helped me out so much lol thank you

[@brianmclogan]

you are very welcome!

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Sir amazing i am from India thank you sir

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Sir you are great thank you very much

[@brianmclogan]

you are very welcome!

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Thank you so much good sir.

[@brianmclogan]

you are very welcome!

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Finally I cleared my doubt with the help of eight year's old video...

[@meenalgautam1465]

thanks

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[@__MoNu966]

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[@may-annemalunes8831]

hi! I just want to ask how did you get the p?

[@rafaelleuterio7900]

i like how there's a point of whiteboard marker ink on his head pretty chique tbh

[@lapetitefleur3482]

But what if the focus has a fraction

[@chambinabi9646]

Believe us. Thank you. I feel sorry for my parents if they found out that I've learned from KZbin not in my University 😂. Thank you so much sir!

[@brianmclogan]

haha, happy to be there for you

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Hey we have the same last name

[@chambinabi9646]

@@cledlirahariola7454 Hey waddup! Studying for Online Class?

[@cledlirahariola7454]

@@chambinabi9646 yup

[@lutaradnus6481]

thankyou

[@asiabibi1100]

Where can i get teh entire playlost

[@jazminarenas3089]

i’m a bit confused, your description says (x-h)^2=4p(y-k) is for parabolas that open left or right but you used it in the video and the parabola opened up

[@Burgerkingfootlettuce456]

For the (x-2)^2 portion, how did you get x^2 -4x-+4?

[@luci316]

i was wondering this too but this comment is a year old :(

[@monke8568]

@@luci316 he expanded it making it (x-2)(x-2) then solving to x^2-4x+4

[@Goku-dk9md]

Man is white Randy Orton

[@ronitsinghpatel5319]

love from india

[@sasinmo]

Is the focus above and the directrix always behind the vertex of the parabola?

[@brianmclogan]

not always above, because the parabola can open down left and right as well. Just remember that the parabola always opens towards the focus and the directrix is the opposite direction perpendicular to the axis of symmetry

[@noni6513]

What if some of the given is negative?

[@dragonandtokkikwonpark4643]

Watching this 5 am before the examination 🤦🏼‍♀️

[@andrewmiguelgrande3062]

Same

[@kristinea.7826]

lmao, good luck btw, did ya pass?

[@midaskun7556]

What if it opens to the right?

[@jathinreddy460]

U saved me man

[@brianmclogan]

happy to be able to help

[@michaelamaemojica837]

Hi guysss, may I ask how did the professor get the 3 beside the 4 and it becomes 4(3)

[@shhmelloww5382]

The letter p represent the distance between the focus, vertex and directrix. The focus is (2,4) and the vertex is (2,1) we only need to focus on the y, which are 4 and 1. You will need to count the spaces in between the focus and vertex which is 3 spaces. So you just plug in 3 where the p is and get 4(3); 12

[@pauleenignacio6487]

What to do if my vertex is at (0,0)

[@VA7504]

If h (2) in the vertex is the same as h (2) in the focus, use the vertical form.

[@ivangamayao1738]

Sir. Why do you plus both side by 12?

[@brianmclogan]

to isolate the y

[@erbazkhan266]

Can you make a video for Parabolic comet problems?

[@brianmclogan]

+Rainman 10 sorry I am not teaching that this year