I'm in Calculus 2 and no teacher has ever taught me how to complete the square. Thank you for teaching me all the things all my many teachers over the years have missed or skipped over.
These videos blow Khan Academy out of the water. Thank you my friend. I've always "done quadratic equations" but never knew the definition. Now I'll never forget it's a 2nd degree equation.
I am 67 years old. 50 years ago when i took intermediate, i was helpless. Got through with Cs basically with dumb luck. I found your channel by accident, and now I am in 11.2 and actually know what I am trying to do. Why am I doing this? Who knows, but its fun. If you had been around in 1968, i may have been a superstar in class.
One motivation for learning math, other than for pure fun, is that it can be helpful in everyday life when you least expect it. You become a lot more flexible with all kinds of things if you can perform mathematical calculations on stuff. And of course, it is very mentally stimulating as well.
I need to send this beautiful man a gift. With his help I went from a "C" on my first exam to a 98/100 "A" on my second exam. 3rd exam is tomorrow and I'm confident to the gills--a lot of thanks due to professor leonard. Seriously, I'll donate to your favorite charity or whatever, just email me. Thank you so much for the help.
What a great idea. You are taping your own lectures and extending your audience to the Internet. You aren't motivated by tutoring fees or other charges since you already making a living as a teacher. Nice guy!
The proof circa 12:00 is amazing. Learned a lot of little things that I had forgotten, understood only in the most superficial sense, or never learned at all skimming through this course and stopping at the relatively unfamiliar parts 10 years after first taking calc 1 (complex numbers, imaginary numbers, completing the square). Thanks man.
"The last thing we gotta do is write out both of our solutions... which we have two of" hahaha. I love the repetition... feel like I've internalized these concepts such that I may never have to give myself another "algebra refresher" again.
Hey Prof, I've been watching your videos to supplement my studies through Khan Academy. Sometimes they don't quite explain it as well as you do, so many thanks! You're especially a life saver because you explained the quick way to see if "completing the square" is efficient (leading coefficient 1, and b term even). And in the light of contributing education I thought that I might make a suggestion that might make explaining everything a bit easier and maybe allow your class to start answering the question than you doing it over and again. Here it is: What if, towards the beginning of the lesson you show the proof of what you're doing ("divide by 2 and square it, reuse it later"). What I mean is to leave on the board the Perfect Square Trinomial [(x+g)^2 = (x^2) + 2(g)(x) + (g^2)]. Now the important thing with this is that you leave it up on the board for a few days so that everyone can see that when you're trying to create a Perfect Square Trinomial in the General Quadratic Form of [a(x^2) + b(x) + c = n] Then you can point out and demonstrate that when your trying to do this... The Formula we're creating = Formula we Have [(x^2) + 2(g)(x) + (g^2)] = [a(x^2) + b(x) + c]
I have a hard time with the board at Khan Academy. The colors and blackboard are distracting and I can hear the clicking of his pen. This lecture is more real to an actual classroom since it is an actual classroom.
the quadratic formula intimidates and frustrates most people that have to deal with it, but professor Leonard was able to simplify it into an easily digestible and understandable idea. That's among the best compliments any math teacher can get and I will forever be in debt to this mans amazing teaching abilities. Thank you professor.
The last 10 minutes of this video are the most important. He shows that way that the quadratic formula was invented. You can understand how early mathematicians finally figured out how to solve second degree polynomials.
Maybe you will never read it, but you became part of my life and probably also part of a lot of others peoples life. Somehow you changed the world for the better. Better than politicians could ever do 😉 Thanks a lot for your very appreciated math lessons! ❤️
that was what i was thinking about , in middle school i changed my class to be in the same class of the girl i loved but if i had leonard as a teacher i would just be in leonard class xD !
Great video and I got this Intermediate Algebra practice test on quadratic equations and inequalities. I will to watch the rest of your series so that I can master pre-calculus.
Omfg ❤️❤️❤️😱 lmao! I never knew that the quadratic equation was derived from “completing a square” of a quadratic equation. That’s was so beautiful! ❤️ ... Im a Chemistry major and masters. By this right here was amazing!
wow, you made me understand where the quadratic formula comes from, that's really awesome! I wish my teachers would've taught me math logically instead of spilling some meaningless formulas on the table
Professor Leonards, you are a brilliant math teacher with a brilliant mathematical mind! You explain everything so clearly that it would be difficult for me to NOT understand something. Every time I watch one of your videos, I understand more and more of what I'm learning about. I have major difficulties with math, so your math videos save me every time. P.S I have problems with proving triangles and with sin, cos, and tan. They currently cause a lot of difficulty for me. Do you have any videos elucidating on proving triangles AND sin, cos, and tan? Thanks!
I was also struggling with trigonometry till I used Auffman, Barker and Nation's seventh edition of College Algebra/Trigonometry, but Trigonometry Demystified works too.
In middle school i changed my class to be in the same class of the girl i loved but if i had leonard as a teacher i would just be in leonard class xD !
Out of curiosity, what grade level is this class? High School? College? I am taking Intermediate in Community College, which is a General Education requirement for an AA degree.
I'm in Calculus 2 and no teacher has ever taught me how to complete the square. Thank you for teaching me all the things all my many teachers over the years have missed or skipped over.
These videos blow Khan Academy out of the water. Thank you my friend. I've always "done quadratic equations" but never knew the definition. Now I'll never forget it's a 2nd degree equation.
I am 67 years old. 50 years ago when i took intermediate, i was helpless. Got through with Cs basically with dumb luck. I found your channel by accident, and now I am in 11.2 and actually know what I am trying to do. Why am I doing this? Who knows, but its fun. If you had been around in 1968, i may have been a superstar in class.
One motivation for learning math, other than for pure fun, is that it can be helpful in everyday life when you least expect it. You become a lot more flexible with all kinds of things if you can perform mathematical calculations on stuff.
And of course, it is very mentally stimulating as well.
I need to send this beautiful man a gift. With his help I went from a "C" on my first exam to a 98/100 "A" on my second exam. 3rd exam is tomorrow and I'm confident to the gills--a lot of thanks due to professor leonard. Seriously, I'll donate to your favorite charity or whatever, just email me. Thank you so much for the help.
So how did you do
The last 15 min of the video is a life saver...excellent teaching. Wonder were he learned how to teach like that or if he is just a natural?
its because he loves math and he understands logic
What a great idea. You are taping your own lectures and extending your audience to the Internet. You aren't motivated by tutoring fees or other charges since you already making a living as a teacher. Nice guy!
The proof circa 12:00 is amazing. Learned a lot of little things that I had forgotten, understood only in the most superficial sense, or never learned at all skimming through this course and stopping at the relatively unfamiliar parts 10 years after first taking calc 1 (complex numbers, imaginary numbers, completing the square). Thanks man.
You are the BEST! Just made Math so fun and easy!!
"The last thing we gotta do is write out both of our solutions... which we have two of" hahaha. I love the repetition... feel like I've internalized these concepts such that I may never have to give myself another "algebra refresher" again.
Hey Prof, I've been watching your videos to supplement my studies through Khan Academy. Sometimes they don't quite explain it as well as you do, so many thanks! You're especially a life saver because you explained the quick way to see if "completing the square" is efficient (leading coefficient 1, and b term even). And in the light of contributing education I thought that I might make a suggestion that might make explaining everything a bit easier and maybe allow your class to start answering the question than you doing it over and again. Here it is:
What if, towards the beginning of the lesson you show the proof of what you're doing ("divide by 2 and square it, reuse it later"). What I mean is to leave on the board the Perfect Square Trinomial [(x+g)^2 = (x^2) + 2(g)(x) + (g^2)]. Now the important thing with this is that you leave it up on the board for a few days so that everyone can see that when you're trying to create a Perfect Square Trinomial in the General Quadratic Form of [a(x^2) + b(x) + c = n] Then you can point out and demonstrate that when your trying to do this...
The Formula we're creating = Formula we Have
[(x^2) + 2(g)(x) + (g^2)] = [a(x^2) + b(x) + c]
I have a hard time with the board at Khan Academy. The colors and blackboard are distracting and I can hear the clicking of his pen. This lecture is more real to an actual classroom since it is an actual classroom.
the quadratic formula intimidates and frustrates most people that have to deal with it, but professor Leonard was able to simplify it into an easily digestible and understandable idea. That's among the best compliments any math teacher can get and I will forever be in debt to this mans amazing teaching abilities.
Thank you professor.
The last 10 minutes of this video are the most important. He shows that way that the quadratic formula was invented. You can understand how early mathematicians finally figured out how to solve second degree polynomials.
Maybe you will never read it, but you became part of my life and probably also part of a lot of others peoples life. Somehow you changed the world for the better.
Better than politicians could ever do 😉
Thanks a lot for your very appreciated math lessons! ❤️
This teacher completely changed me from zero to hero in Whole algebra
These students are blessed to have you as their professor.
that was what i was thinking about , in middle school i changed my class to be in the same class of the girl i loved but if i had leonard as a teacher i would just be in leonard class xD !
Great video and I got this Intermediate Algebra practice test on quadratic equations and inequalities. I will to watch the rest of your series so that I can master pre-calculus.
Omfg ❤️❤️❤️😱 lmao! I never knew that the quadratic equation was derived from “completing a square” of a quadratic equation. That’s was so beautiful! ❤️ ... Im a Chemistry major and masters. By this right here was amazing!
wow, you made me understand where the quadratic formula comes from, that's really awesome! I wish my teachers would've taught me math logically instead of spilling some meaningless formulas on the table
Thnks professor ...you are truly a magician
Nice explanations! Lots of help.. Thanks for posting!
Thank you so much .So easy to understand .
you're helping me a lot on my tests! hugs from Brazil.
Professor Leonards, you are a brilliant math teacher with a brilliant mathematical mind! You explain everything so clearly that it would be difficult for me to NOT understand something. Every time I watch one of your videos, I understand more and more of what I'm learning about. I have major difficulties with math, so your math videos save me every time.
P.S I have problems with proving triangles and with sin, cos, and tan. They currently cause a lot of difficulty for me. Do you have any videos elucidating on proving triangles AND sin, cos, and tan? Thanks!
Hi, I don't have those videos yet, but they will be coming some day :)
I was also struggling with trigonometry till I used Auffman, Barker and Nation's seventh edition of College Algebra/Trigonometry, but Trigonometry Demystified works too.
you explained so well
I owe this man alot
Thank you soooo much professor , you are the best
The literal god
Why can't it be next to 3i...like 3i-+2 42:11
Good teacher!
Omg prof tysm
In middle school i changed my class to be in the same class of the girl i loved but if i had leonard as a teacher i would just be in leonard class xD !
30:52
1:07:20,Professor Leonard GOES GANSTA
I can finally understand math
Out of curiosity, what grade level is this class? High School? College? I am taking Intermediate in Community College, which is a General Education requirement for an AA degree.
What book do you use?
I suppose it's McDougall Littell, they make very good math books. Mine is "An Applied Approach" from Auffman/Barker/Lockwood.
@@luciusirving5926 The Textbook is "Beginning and intermediate algebra by McGinnis, Terry Hornsby, John Lial, Margaret 6th or 5th edition"
I honestly prefer Completing The Square over Quadratic Formula.
35:09 was a good one hahaha
Khan Academy does not have any silicone injections in their breasts or their arms
I love you
fuarkkkkk
Long story explaining not enough
Rough way of teaching cos of speed