how to find the vertex of a parabola (completing the square vs. derivative power rule)

[@blackpenredpen]

For more algebra tutorials, please see my new channel "Just Algebra" 👉 bit.ly/just_algebra

[@PerfectlyCrafted]

Really great calculus explanation! I couldn't have done it better

[@blackpenredpen]

Thanks!!!

[@v-lt9wy]

Even after 6 years, im so thankful to you my man. This is the type of explanation I wish every teacher gave, not just for calculus but for everything. Would make everything possible literally. Thank you so much man!

[@tarat.techhh]

BLACKPENREDPEN YAY!!!!!!!!!!!!!!!!!!!!!!! everyday you proves that maths is damn interesting.

[@blackpenredpen]

Cheesysins and Cheezysins thank you!!!!!!! I am so glad that you like my videos and it's my pleasure to continue make videos for you!!

[@tarat.techhh]

well its a pleasure to watch your videos..and thanks for uploading constantly. Maths is my favourite subject.I have completed my high school last year and i think now i am enjoying maths more than i used to do earlier just because of you....so thanks.. also could you plz do some more videos on permutations and combinations..

[@sansamman4619]

at 4:28 the number will always be the magic number before you square it ( 1/2 the coefficient of x )

[@blackpenredpen]

San Samman yes!!

[@vihanprashant9702]

Great work!

[@_deleted_12472]

Hey, I love the video Steve! Usually I don't comment, but I think I know a more intuitive way to find the vertex using symmetry. Since moving the same horizontal distance left or right from the vertex puts you at the same height on the parabola, but ONLY from the vertex, let f(x-h)=f(x+h) where f(x)=ax^2+bx+c. Then x=-b/(2a) falls out immediately.

[@blackpenredpen]

YoshisToadies oooh!!! That's very nice!!! Thanks

[@sardarbekomurbekov1030]

I really like your explanations)))

[@blackpenredpen]

Thank you!!!

[@everglade7764]

Thank you!☺️

[@wahyuadi35]

Your explanation and your accent is just nice. I like it.

[@oldhackee3915]

Excellent!

[@TitoTimber]

Thanks, it helped a lot.

[@lffb8803]

now got here with 0 view! finally

[@blackpenredpen]

Not just that. I will also pin you!! Congrats!!! YAY!!

[@lffb8803]

thanks :D

[@MarathiAsvad]

Bro unpinned

[@thesinglemathnerd]

Awhile ago I found the formula to find the one local minimum and one local maximum of a cubic function. If you follow the steps of the derivation of the quadratic formula after taking the derivative of the cubic function in standard form and after some nice simplification you will arrive at x=(-b+-sqrt(b^2-3ac))/3a. And obviously you check the values of the derivative of the function around those points to determine which one is the minimum and which other one is the maximum.

[@blackpenredpen]

Nathodood lol that's exactly what I am recording right now!!!

[@blackpenredpen]

Nathodood so 😎

[@thesinglemathnerd]

blackpenredpen haha is the method I described identical to the calculus method you will show?

[@blackpenredpen]

Nathodood yes!

[@thesinglemathnerd]

blackpenredpen I knew it! I can’t wait to see it!

[@carlosrosales1712]

You’re amazing!! :)

[@RutvikPhatak]

I once more put forth the motion to bring back the "Black Pen Red Pen yay!" back. Even though I love doaremon I love that way more and it's also iconic for the channel! P.S.- great video!

[@OonHan]

Within hours you already have 1000+ views! ;) ;) ;)

[@shuidongliu954]

Amazing video as always! Just wondering if you could do a video on: integrate 1/(1 + ln(x)) dx Or if not, could you reply in the comments? Just a question my maths teacher set me, and it's really grinding my gears not knowing how to do it!!! Thanks! Keep up the great videos!!!!!

[@blackpenredpen]

Lewis Clarke hmmmm I don't think there's an answer for that

[@prashantdubey9430]

this is a good one

[@115Carssssssssss]

There is also a method to prove without calculus Let α and β be the roots of equation ax^2+bx+c=0 x^2+(b/a)x+(c/a)=0 Since a quadratic equation is can be written as x^2-(α+β)x+αβ=0 So α+β=-b/a αβ=c/a Since the vertical line which passes through the vertex is the axis of symmetry So the equation for the axis of symmetry is x=(α+β)/2 x=(-b/a)/2 x=-b/(2a) Therefore the vertex is at x=-b/(2a)

[@yousefnoori]

You used Vieta's laws out of the blue, now prove Vieta's formulas. :p

[@gesucristo0]

Could you do some videos about riemann's hyphotesis please?

[@user-sb6os]

Thanks

[@prashantdubey9430]

we can use the second derivative and punch i the value of x and y and see whther its negative or positive. we can do it that wayas well. correct me if i am wrong

[@Craznar]

Damn, was hoping for a vortex formula.

[@blackpenredpen]

Christopher Burke r u ok?

[@Craznar]

Nah, but that's life sometimes. Your videos always make me feel better though. So - next video is the vortex formula ? LOL

[@blackpenredpen]

well.. i am not sure about vortex, but here's the wikipedia page en.wikipedia.org/wiki/Vortex

[@blackpenredpen]

densch123 we have to wait for Chros to reply.

[@Craznar]

Was just a joke ... vertex vs vortex .... that's all. I suspect a full vortex formula is outside the scope of a youtube video :)

[@gongasvf]

Here’s a limit I found fun, if you want to give a try: limit as x tends to +infinity of (n/(n+1))^n

[@blackpenredpen]

Nice! I actually have the video on it too kzbin.info/www/bejne/rJispGSEe5dpoNU

[@DavidC2718]

I love you sir

[@mandwaleadi775]

Why do we differentiate equations ?

[@mukhammadrizomadjidov5136]

I have a question that if x is set 0 for example, isn't 0^0 defined? because when we take derivative of linear term we are kind of using that fact

[@XESolar]

This is relevant to what I am studying for my maths final isn't it?

[@blackpenredpen]

Connor Marriott depends on your class, isn't it?

[@zouraizkhan2467]

know im late but rocking that look

[@TheShutteredRoom]

And this is also the secret to understand why the statistical mean is the sum of all parts over the number of parts.

[@avananana]

So I found a problem I couldn't solve and was wondering if you could attempt to solve it, it's abit above my knowledge but I don't think it's that hard. A quadrilateral under the graphs y = e^x and y = (5 - x), one of its corners are located on the e^x function, and the other corner is located on the (5 - x) function. Its other two corners are located along the x-axis. Its area never stretches beyond the function limits nor does it go under the x-axis. What is the maximum possible area of the quadrilateral? I for some reason cannot find a solution to this problem.

[@sylvd81]

More basically... 😉 Solve f(x0 + h) = f(x0 - h) where x0 is the abscisse of the vertex, it's like an odd function. And you'll find x0 = -b/(2a)

[@GGGGAMER]

What does settiIng 2ax+b to 0 even do? What if we set it to 1, would the answer change?

[@harmannd7270]

GGG GAMER 2ax+b=0 is the derivative of a quadratic , since the slope the of the tangent line at the vertex of a parabola is 0, we set the derivative = 0

[@yousefnoori]

If it was set to 1, that means you will find the value of x where the derivative (slope/ rise over run) is equal to 1, which is not the vertex. It depends on the shape of the parabola but it's generally a couple of units from the vertex maximum, still not the vertex.

[@Notyouranalyst]

Hey BP could u please explain why only by (b^2/4a^2)...why only that to be added... Please help me out dood

[@zeusequinox602]

Can you solve this ? Find inverse of ax^2 + bx + c = f(x) from -b/2a to b/2a

[@clawsie5543]

you just need to complete the square. y=ax^2+bx+c y=a(x+b/(2a))^2+c-b^2/(4a) x=+/- sqrt(y/a-c/a+b/(4a^2))-b/(2a).

[@Metalhammer1993]

That's a brilliant intro to calculus. Probably gonna use this for my tutoring students to get them to get the idea behind extreme values. The pen trick is just world better than my motorcycle image. (The basic idea is the same just a bit more lively but maybe a bit to lively. I have them imagine we drive through a mountain range on a motorcycle. First we ride up meaning yeah we are really going up than at the peak of a mountain before we go down, we are vertical before going down. And down there in the valley we too have the bit we are not going down anymore. The pen thing just is simpler

[@OonHan]

#oreo

[@gnikola2013]

The problem with this algebraic way is that you rely on the fact that you know the canonic expression for the parabola. If you didn't know it, you can also find the X value of the vertex by analising the cuadratic formula. You'll get only one result if √(b^2-4ac) = 0, and the result would be precisely -b/2a

[@OonHan]

I don't understand what a vertex formula of a parabola. Please explain???

[@blackpenredpen]

Oon Han it tells u the highest or the lowest pt of the parabola.

[@blackpenredpen]

Oon Han I am working on the vertex formula for cubic next.

[@OonHan]

you mean a minimum or maximum?

[@OonHan]

well, using calculus is the same!!! find the inflection point of the cubic.

[@blackpenredpen]

Oon Han yes

[@algirdasltu1389]

When calculus is easier than algebra:

[@gurjeet4604]

Doraemon theme at intro?

[@blackpenredpen]

yes

[@AnvitGarg25]

Haha, my sister thought I was watching Doraemon

[@feroch8901]

Hello sir, Can I know how did you conclude that 'h' and 'k' are the value of x and y at the vertex respectively in equation : y=a(x-h)+k Note: if anyone reading the comment section knows the answer to this please hare it with me it will help me alot and I will be very grateful for it😊 Thank you

[@OonHan]

2^7th view! lol

[@sojulia1990]

The calculus way was easier, you just have to find the derivative, set is equal to 0 and find x.

[@wellbangok8959]

I got my first C+ in a math class. Screw you linear algebra lmao.

[@semiawesomatic6064]

It's over Anakin, I have the high ground. Oh man, I hated linear algebra. It was so... Tedious? Boring? Mind-numbing? Yeah that last one :P

[@Gold161803]

Take DiffEq and your opinion might change. Haha

[@wellbangok8959]

Gold161803 I have, Diff EQ wasn't nearly as bad. My linear algebra class was basically all proofs.

[@Drytube]

Let's say the first derivative of the quadratic function, ax^2 + bx + c, is equal to 2ax + b. We know at y = 0, we will find the local maxima or local minima. But, what does x = 0 represents there? i.e y = 2a(0) + b => y = b. What is the importance of x values in the first derivative, we know that we can set the y' to 0, in order to calculate blah blah blah. But what about x?

[@jeffeloso]

Half the sum of the roots.

[@unrulyObnoxious]

Calculus won't work for a slanted parabola. ;-)

[@semiawesomatic6064]

Nilabro Saha P A R A M E T R I C

[@unrulyObnoxious]

semi awesomatic Ooooo.... Never thought about that. xD my bad. I've gotten too used to just using the cartesian equation!

[@semiawesomatic6064]

Nilabro Saha it's cool. I actually skipped my precalc class, so I don't know exactly how you'd go about using parametric :P I could probably do it but meh. Just an idea :P

[@steb430]

Great, Isn't it!

[@ankitchauhan8682]

love doraemon😂

[@matthewmazurek]

Part 2 is here (link broken above): kzbin.info/www/bejne/aXfMfXefl7R3adU