Graphing Conic Sections Part 3: Parabolas in Standard Form

The parabola is back! I know we've learned a bit about these, but they are one of the conic sections, so let's go a little deeper and learn some new ways to define a parabola. Also, we know how to graph these in vertex form, but we haven't learned how to graph them in standard form, so let's take care of that too, while we're at it!

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!

[tmchannel]

I felt slightly overwhelmed during this video for the first time in the series but actually got all the comprehension questions right on the first try. That boosted my confidence for sure.

[bomaathuis]

If anyone is having a hard way doing this to get the local minimum or maximum (coordinates of the vertex) go check prof Dave’s videos on differentiation. If you take the first derivative of the function and set the answer = 0 and solve for X you get the x value of the local minimum or maximum you’re looking for. When you plug that into the original function for x you get the y value of the coordinate of the vertex. Thank you prof Dave for learning me all of this.

[PalasBrown]

as always, thank you professor dave for the math knowledge

[kenyamane]

That odd satisfaction from the intro song doesn`t get old.

[aminnima]

If only we were thought math this way in schools... Thank u sooo much sir you are a star

[ItsMe-icoc]

Hi Professor Dave, thanks for the lesson, I have a question (sorry for bad English):

In order to go from vertex form back to standard form, do I use the (x +- h)^2 = (x^2 +- 2xh + h^2) formula, and then multiply every term by a? Also, is it correct to say (based on the formula) that to go to standard form from vertex, a = a, b = -2ah, c = ah^2+k ?
Thanks in advanced, I missed this lesson because of the virus.

[alexmirzabdullaev]

How does 1 in c became 2 in completing the square manually

[melkinouha]

hello bit confused there the standard forms of parabola like y2=4ax how can relate both of them ? sorry it may seems a dum question !

[kamrankhanUSA]

This video is not helpful like circles and eclipses

[harishs]

Professor to find vector form from parabolic form in strategy 1 you have added b^2/4a into the parentheses that has been multiplied by a, But whereas outside u have subtracted b^2/4a instead of ab^2/4a

[RadoHudran]

Great feeling when I understand something 3 years after they tried to teach it to me in school

[zgmg]

If you're stuck on this one try starting with problems 2 and 3 before 1. 1 is trickier because of the 2x^2 and - 4x

[theguythatdoesmath]

when i saw x^2 and derivatives in an algbera II course, i was like, what, i thought this was algebra II?

[anilkumarsharma]

What is length of the parabola curve between any two points
What is line equations for that length
How they are correlated

[reenithafrancis]

Thanks for the vid pls upload moree you also got my subscription

[alexmirzabdullaev]

I finally got this fast-pace topic after watching hours of lectures on YouTube

[akram]

6:07, how did you plot the x intercept values? Prof. Could you xplain it further?

[ystyphnboth]

Why the a in c-b²/4a isn't squared?

[satyamohanty]

1:07 I didn't understand what the word "derivatives" was doing there on the bottom right.

[heysharty]

3:24 why don't we subtract a times -b^2/4a since its being multiplied by a