Deriving the Quadratic Formula

[Misterlikeseverythin]

Why do math teachers in high school never show how to prove stuff. They just say here's the formula now DO MATH. Takes out all the fun out of math. No wonder so little people in my class like it.

[ChrisBrownLvr]

I can't believe I was never taught this. Thank you, puts some meaning into the formula.

[terrygale]

Great explanation! In high school I remember deriving this but that's been over 50 years and now I'm teaching my grandchild so I wanted some reminders.

[sivad]

Omg thank you! I started giggling when it all worked out

[KillianDefaoite]

THANK YOU THANK YOU THANK YOU A MILLION TIMES!!! THIS WILL BE ON MY MATH FINAL EXAM I CANNOT THANK YOU

[patrickjmt]

aww thanks : )
glad i am able to help a bit

[mirasur]

Thank you so so much for making this video! I was really confused when my math teacher explained this concept today, but your video has really helped me clear things up.

[patrickjmt]

well, completing the square is basic high school algebra...

i think most any decent hs algebra student could follow this

[mountcarmel]

The question suddenly came into my mind as to where the quadratic equation driven from, just go to you tube and find you there. Awesome! Thank you.

[patrickjmt]

@azk2020 well, often times people want to know why something is true. showing why something is true (some formula) is usually much more difficult than showing how it is used. i think just about everyone has seen the quadratic formula by high school, so i think it is rewarding to know where it comes from : )

[عبدالالهاليمني-مع]

Deriving is the best lesson for me, I love to deriving in mathematic.

[Thor_with_Ball_Hammer]

I am 30 now and this question popped up in my mind while solving 2nd degree polynomial equation without calculator that how this formula arrived. In school and college i didn't have enough time to question my self how this formula arrived. Now I m an electrical engineer in power generation company. Thank you sir that was pretty impressive 👍😊.

[patrickjaegers]

Great vid! My math teacher in Algebra 1 my freshman (1989) year had us practice completing the square every day for weeks. After doing the repetitive task several times, I knew there had to be a formulaic way to get the answer. So one evening I went home and figured it out exactly as you showed here. I went to school early the next day to wait for my teacher to get there to show him what I discovered. I was very excited because I thought I was going to get my name on a function that hadn't been discovered yet. He was extremely impressed that I figured it out, and then smiled and had me flip my algebra book ahead a couple chapters to the quadratic formula. While he was excited for me, he totally let the wind out of my sails. Three years later when I was a senior, he wrote an incredible letter of recommendation for me when applying to a university to study Actuarial Science. I got accepted with a very nice scholarship to boot!

[cole]

Genuinely thank you so so so much. I was stressing over this earlier today and now I have no worries about it and I fully understand the concepts. Thank you again.

[agrofindastation]

I remember how cool it was in 7th grade to go though this in my math class. This brought back such a great memory.

[noble]

I'm an 8th grader this year and we have to take a test tomorrow over Ax^2+Bx+Cx and finding the quadratic formula. I am grateful for this video!!!😄😄😄

[ApexMark]

3:24. I keep forgetting what I'm actually needing to add back in! I kept adding b^2/4a^2 to the right side. All the other examples online I found took the a across as the first step so I wasn't able to discover my problem. Thanks! This often catches me during completing the square - neglecting to pay attention to the constant outside the parentheses when deciding what needs added back in.

[YuKal]

Thanks alot for this, your probably the best teacher teacher on youtube and the you would own the math teachers at my school!

[kyedefriend]

Thank-you so much for this. It was set as homework and I made so many 'silly mistakes' which meant before I watched the video I had spent hours trying to complete it myself. You have 'showed me the light'!

[ScorpioHR]

After 20+ years of wondering, I finally got focused enough to actually look this thing up. As someone who tries not to take things for granted, this bothered me for decades. But it would only be flashes I would end up ignoring. Today was the day I said: NO MORE!



It's fascinating how it all fits perfectly after the "perfect square" gymnastics. Like, the same denominators on both sides made it smooth.

Math is magical, too bad I was kind of an idiot in youth and gave up on education