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You are very welcome Mathison! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃
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To be honest, I really love the way you explain it step by step! now I can solve quadratic equations by heart. Keep up the good work🙏❤️ greetings from PNG🇵🇬
You are very welcome Cristine! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
You're very welcome! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Kind regards :)
You are very welcome! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
You are very welcome Kimala! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
You are very welcome Aliyaha! You are so generous. I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
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Thanks! My teacher explained it 3 or 4 times but I didn't understand. But you explained it just 1 time and I understand. Today I have assessment from it. I'm so happy!!!
You are very welcome Jahongir! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Thank you so much! Your explanation is way better than my maths sir as he goes through everything quite fast and its hard to understand but you go through it slowly and its like your making sure that we understand so thank you🥺
You are very welcome! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Original equation is y = 2x² -4x -1. This is standard quadratic form where y = ax² + bx + c We want it in vertex form which is y = a(x-h)² + k. h is obtained with the formula h = 1/2(-b/a) the k is obtained with the formula k = -a(h)² + c. h = 1/2(4/2) which is 1 k = -2(1)² - 1 which is -2 * 1 - 1 or -3 y = 2(x-1)² - 3 We now have the xy coordinate of the vertex which is [1 , -3] the xy coordinate of the y intercept is always the c value. [this can be any real number] which is [0 , -1] Now we need to find the x intercepts [ Note: If the k value is the opposite sign of the a value there should be two x points on the x axis where the parabola is formed] x = h + √(-k/a) and x = h - √(-k/a) [the √ symbol applies to both the k and a terms] x = 1 + √(3/2) and x = 1 - √(3/2) Irrational denominators we must multiply √3 * √2 and √2 * √2 This gives us : x = 1 + (√6) / 2 and x = 1 - (√6) / 2 So the x intercepts are [1 + (√6) / 2 , ] and [1 - (√6) / 2]. or [-0.22474487139 , 0] and [2.22474487139 , 0] (If not obvious these are two sets of xy coordinates which is why the y part is 0) Finally since the a term is positive it is an "Up wards" parabola. Quadratic formula is very clunky and isn't needed if you are working with the vertex form. The hardest part of this specific problem is converting the x intercepts to decimal form.
You are very welcome Prachi! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
So nice of you Vladimir! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃 Have a very happy and blessed New Year!
You are very welcome Maab! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Have a very happy and blessed New Year! Keep smiling😊
You are very welcome! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@@tylerdurden3987 Because, like Sherlock Holmes, he puts together bits of information and reaches the solution. Are you just having a bad day durden, or are you so thick you can't see this for yourself? You clearly lack the intelligence to be good at maths or at anything that requires a little bit of logic. Have a nice day!
Glad to hear that Fatima! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Excellent, only minor remark is I can not distinguish a and 2 sometimes. Can you please write the cypher '2' a bit different so I can see the difference with the letter 'a' better. Thank you in advance.
Hi again...Could you do a video on Graphing a quadratic equation that has Imaginary roots/soluitions? y=6x^2-7+8 for example.and discuss graph difference from one with real roots. Thanks.
Glad to hear that Aiman Beti! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and stay blessed😃 Keep smiling😊
You are very welcome Ren! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
look at my comment above, I just posted it before posting this. I find the quadratic formula very clunky and hard to remember. I used a dumbed down alternative to it.
By seeing you, even, I have to teach someone. You are God for students like me . By heart , I can't say something. Everyone want to you to have their read.
You are very welcome Ved! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
You are very welcome Kuminyanga Gomani ! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and stay safe😃
Your videos is so very good and clear everytime i watch it, you know even if the equation is so hard once i watch your vid. Like omy-- Everything is so clear and easy. Thanks to a good teacher like you!❤
You are very welcome Nathalie! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and stay blessed😃 Keep smiling😊 Enjoy every moment of your life 🌻
You are very welcome! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
2*x^2 - 4*x - 1 = 0 : a = 2 , b = -4, c = -1 ; c/a = -1/2: m = -b/(2*a) = 1: m^2 - d^2 = c/a; d = sqrt( m^2 - c/a ) ) = sqrt( 1+ 1/2 ) =sqrt( 3/2 ); Roots are ( m - d ) and ( m +d ) Easy to verify that R1+R2 = 2*m and R1*R2 = (m - d )*( m + d ) = m^2 - d^2 R1 = m - d = ( 1 - sqrt( 3/2 ) and R2 := ( 1 + sqrt( 3/2 ). For vertex : xV = m = 1 ; yV := f( a,b,c,xV) = f( a,b,c,1) = a + b + c = -3; And this will work for cases where a,b,c are real numbers which include integers [ as here ], rational numbers, prime numbers even irrational numbers. In view of this canonical method I've always wondered why simple quadratics are such a popular topic in even elementary algebra.
dear Andrew, the graph will always intersect at any point on y-axis. However, it it doesn't intersect x-axis, then NO real solutions! Thanks for asking😀 Take care dear and all the best😃 Have a very happy and blessed New Year!
You are very welcome dear! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
anyone know y=x^2 and y=-x^2+4, i thought when we reverse the sign of x it reflects in y-axis , but why this graph is reflecting in x-axis?, kindly clarify
Thanks so much for this now i finally understand my teacher just yells at me when its him who is bad at explaining 😂 literally no one in my class understands so thank you sir
So nice of you dear. Please keep sharing premath channel Thanks dear for the feedback. You are awesome 👍 Take care dear and stay blessed😃 Love and prayers from the USA!
Oh my gosh, I’ve been struggling with this and my teacher doesn’t explain it well. This guy is a good teacher👍
Thank you so much Neta for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@@issacwesley3599 lol y’all r funny
Naruto fan
😊
Learnt it like drinking water 😂😂 watching from Zambia
Your explanation about solving quadratic equations was so clear and easy to understand..now, I am ready to teach my daughters..thanks so much...
You're very welcome, Martin. Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Sorry for the late response. Best regards :)
this is so wholesome
Your explanation was so clear and understandable.you are a such a better teacher
Can you explain quadratics expression in new videos
This is the best video I've found on this: simple and straight to the point.
I like your videos, you are slow, methodical, and very thorough, and that makes grasping the content good for slow learners like yours truly. Thanks.
You are very welcome Mathison! You are awesome 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃
Bro after 2 days and this genius shows up lifesaver you literally cleared my brain🤓
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Where are you from
Before you ,I was striving with this. All your teaching is always crystal clear
Great video - finally someone ties all the elements of graphing quadratic equations in standard form. Thank you.
Thank you so much! Please keep supporting my channel. Kind regards 😀
the way he says how much is so cute LMAO, *humuch*
ikr LOL
Yeah I didn't pay attention🤣🤣🤣
To be honest, I really love the way you explain it step by step! now I can solve quadratic equations by heart. Keep up the good work🙏❤️ greetings from PNG🇵🇬
Thank you for this video. I was having a hard time with this and it really helps me better understand our lesson.
You are very welcome Cristine! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Hello dear where are you from?
I actually learned something in this, thanks!
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Thank u I'm in online school and it was hard to understand, now I understand it
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Thank you. One of the best explanations I had in months. Hats off for you sir .✔💯
You are very welcome Kimala! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Omg I’ve been trying to figure out my questions for the past 2 hours and you just saved my life thank you so much!! I get it now!! 🙏
Amazing explaination 🎉🎉 Good job
Thank you so much for this video! I've was confused about this topic for a bit, but your video explained everything so clearly.
Thanks so much from Papua New Guinea for your explanation .You just helped me to complete my assignment ❤❤
Me:uses this equation
My teacher:You dare oppose me mortal
🤣🤣🤣
you are a lifesaver 😘
I am from India and I clearly understand your concept and language
who is watching this before their math test lol. THIS HELPED ME SO MUCHHH. I GOT A 90% SO HELPFUL
You teach so good. I like your teaching. I want to be like you .
You read as someone read from PW. The way of your teaching is so good.
oh my god, thank you, i couldn't understand it 2 weeks but understanded it in just 14 minutes, thank you very much
You deserve teacher of the year Thank you so much 😝❤️
You are very welcome Aliyaha! You are so generous. I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃
Have a very happy and blessed New Year!
Thanks for blessing us with the way you pronounce formula 7:50
Thank u for taking your time Sir! 😊
You're very welcome Atangabua Malia Anitoh! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep supporting my channel. Take care dear 😃
Thanks! My teacher explained it 3 or 4 times but I didn't understand. But you explained it just 1 time and I understand. Today I have assessment from it. I'm so happy!!!
You are very welcome Jahongir! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Thank you so much, I’m comfortable to write my test after this lesson.
Thank you so much! Please keep supporting my channel. Kind regards 😀
@Jonathan Melaku why so o.o
Jonathan Melaku or they didn’t get taught so well? So they came here like any other students would
Best teacher I've had in 63 years of studying.
Thank you so much! Your explanation is way better than my maths sir as he goes through everything quite fast and its hard to understand but you go through it slowly and its like your making sure that we understand so thank you🥺
You are very welcome! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
@@PreMath thank you sir😊
ur video made it clearer for me to understand thank you other videos are too confusing
Glad it helped!
Thanks dear for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regard
@@PreMath btw it is kinda weird but i am in 4th grade and i am learning this LOL my self just for fun this type of math is not school work or anything
@@GDCyberHehe Wow. That's incredible 😀
@@PreMath ya ikr XD
Original equation is y = 2x² -4x -1. This is standard quadratic form where y = ax² + bx + c We want it in vertex form which is y = a(x-h)² + k. h is obtained with the formula h = 1/2(-b/a) the k is obtained with the formula k = -a(h)² + c.
h = 1/2(4/2) which is 1
k = -2(1)² - 1 which is -2 * 1 - 1 or -3
y = 2(x-1)² - 3
We now have the xy coordinate of the vertex which is [1 , -3]
the xy coordinate of the y intercept is always the c value. [this can be any real number] which is [0 , -1]
Now we need to find the x intercepts [ Note: If the k value is the opposite sign of the a value there should be two x points on the x axis where the parabola is formed]
x = h + √(-k/a) and x = h - √(-k/a) [the √ symbol applies to both the k and a terms]
x = 1 + √(3/2) and x = 1 - √(3/2)
Irrational denominators we must multiply √3 * √2 and √2 * √2
This gives us :
x = 1 + (√6) / 2 and x = 1 - (√6) / 2
So the x intercepts are [1 + (√6) / 2 , ] and [1 - (√6) / 2]. or [-0.22474487139 , 0] and [2.22474487139 , 0] (If not obvious these are two sets of xy coordinates which is why the y part is 0)
Finally since the a term is positive it is an "Up wards" parabola.
Quadratic formula is very clunky and isn't needed if you are working with the vertex form. The hardest part of this specific problem is converting the x intercepts to decimal form.
Amazing..... indeed excellent
Thank you for the help this really helped me a lot in Algebra. I had no idea what an axis of symmetry was so yeah.
This is one of easiest to follow videos I have seen
Excellent ! . Explained so so well. Thankful to you sir.👌
Your the best teacher thanks to tech me this lesson 😁
Wonderful video. This is the best explanation, yet.
Thank you sir it's really helpful for me.
You are very welcome Prachi! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Wow this explanation is so easy..thank you very much..
Glad you think so!
Thanks for your feedback! Cheers!
You are awesome, Terry. Keep it up 👍
Love and prayers from the USA! 😀
Stay blessed 😀
Great explanation
ITS REALLY HELPFUL ITS EASY TO UNDERSTAND HIS EXPLNATION
So nice of you Vladimir! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends. Take care dear and all the best😃
Have a very happy and blessed New Year!
Omg ,you made everything supper easy , thank you ❤️❤️
You are very welcome Maab! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing premath channel with your family and friends.
Have a very happy and blessed New Year!
Keep smiling😊
Thank so much your explanation was so clearly and interested
Thank you Sir! This was a great lesson and teaching
You are very welcome! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Wonderful, Sir. You make maths exciting! God bless you. To me, you are always the Sherlock Holmes of mathematics!
Sherlock Holmes is a detective. How is this guy like a detective?
@@tylerdurden3987 Because, like Sherlock Holmes, he puts together bits of information and reaches the solution. Are you just having a bad day durden, or are you so thick you can't see this for yourself? You clearly lack the intelligence to be good at maths or at anything that requires a little bit of logic. Have a nice day!
Free University indeed, Thanks teacher
Who's still watching this in 2024 its helping me
This is very helpful thank you very much sir God bless
You are welcome
Thanks for your feedback! Cheers! 😀
You are awesome. Keep it up 👍
Thanku sir for your great help i have understood it easly and quickly
Thanks for the explanation🎉. It was very easy to understand.
that explaination is super awesome sirr!!!
Such a great explanation ♥️
Wow !!!!! your explanation is very clear
Glad to hear that Fatima! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Excellent, only minor remark is I can not distinguish a and 2 sometimes. Can you please write the cypher '2' a bit different so I can see the difference with the letter 'a' better. Thank you in advance.
thanks for your nice step by step explanation
Hi again...Could you do a video on Graphing a quadratic equation that has Imaginary roots/soluitions? y=6x^2-7+8 for example.and discuss graph difference from one with real roots. Thanks.
Hi Vanessa Welles, I'll do that pretty soon. Thanks for asking.
Your explanation is very nice did you take personal tution??
you explained it better than any youtubers understanding everything step by step mean a lot for me thanks a lot
Glad it helped.
Thanks Melkamu dear for the feedback. You are awesome 👍 Take care dear and stay blessed😃
Thanks sir I like the way you teaching steps wise which is really helpful and easy to capture the concepts 😊
glad i found this channel. tqsm
Sir keep it up 🙂 even living is US you are helping us 🙂☺️ keep growing and stay happy 😁❤️
U ain't from US stop lying
Indeed you are an amazing teacher.. explained it perfectly!✨
Good bless you! 😇
Glad to hear that Aiman Beti! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and stay blessed😃 Keep smiling😊
@@PreMath yeah sure
Thank you
Really excellent representation 👌
Thanks for clearing my concept...
the way he says “how much” is so precious omg😭
Thank you so much, I've been struggling with this for a while and this genuinely helped!
Thanks Will for the visit! You are awesome 👍 Take care dear and stay blessed😃 Kind regard
Thank you, this was very helpful and educational! ^^
You are very welcome Ren! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
PreMath thank you. I wish the best for you as well, and ai will share this to my friends.
Complex but crystal clear.
look at my comment above, I just posted it before posting this. I find the quadratic formula very clunky and hard to remember. I used a dumbed down alternative to it.
By seeing you, even, I have to teach someone. You are God for students like me . By heart , I can't say something. Everyone want to you to have their read.
I have a dought question is
Plot the graph of equation y=x²-3x
Thank you so much for explaining step by step how to get those values in a quadratic equation. You saved my life!
Thanks for the vid. But don't we have to firstly calculate the ∆ which tells us if there's a solution or not ?
Thankyou so much sir very nice teaching
You are very welcome Ved! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
hello, I think that you've made mistake in finding x intercept's value in the way of calculating them
yep he did.
BEST TUTORIAL EVER1
You are very welcome Kuminyanga Gomani ! Thank you so much for taking the time to leave this comment. I'm glad you liked it! Your feedback is always appreciated. Please keep sharing my channel with your family and friends. Take care dear and stay safe😃
We can also use the test point method which is much shorter
Described smoothly☺️
Wow this is so Amazing .Thank you sir
Most welcome Jei dear
You are awesome. Keep it up dear 😃
Thanks sir.I got stuck on this question from days.......
It helped so much...
Sir, you are the best. Thank you.
sir, how did it become 4.9? over 4, I didn't understand that part sir, thank you for paying attention to my comment, and it's great to teach clearly.
I don't have the IQ to memorize this
Lamo same
i do i am a nerd LOL
@@GDCyberHehe
Good for you. It's very hard to live with low IQ, but it's just life.
@@iliveinsideyourhouse3943 i know it is very hard
Your videos is so very good and clear everytime i watch it, you know even if the equation is so hard once i watch your vid. Like omy-- Everything is so clear and easy. Thanks to a good teacher like you!❤
You are very welcome Nathalie! I'm sure you are an awesome student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and stay blessed😃 Keep smiling😊 Enjoy every moment of your life 🌻
Thank you so much ❤️❤️🥺
You are very welcome! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
Hey sir I just want to say u thanku so much its really really helpful ☺ u r the best teacher of maths 💖
Bro he sounds like my dentist “open up”
2*x^2 - 4*x - 1 = 0 : a = 2 , b = -4, c = -1 ;
c/a = -1/2: m = -b/(2*a) = 1: m^2 - d^2 = c/a; d = sqrt( m^2 - c/a ) ) = sqrt( 1+ 1/2 ) =sqrt( 3/2 );
Roots are ( m - d ) and ( m +d ) Easy to verify that R1+R2 = 2*m and R1*R2 = (m - d )*( m + d ) = m^2 - d^2
R1 = m - d = ( 1 - sqrt( 3/2 ) and R2 := ( 1 + sqrt( 3/2 ).
For vertex : xV = m = 1 ; yV := f( a,b,c,xV) = f( a,b,c,1) = a + b + c = -3;
And this will work for cases where a,b,c are real numbers which include integers [ as here ], rational numbers, prime numbers even irrational numbers.
In view of this canonical method I've always wondered why simple quadratics are such a popular topic in even elementary algebra.
Thanks a lot Harold for such an awesome feedback!
Stay blessed and healthy my friend😃
Very happy new year
Love you sir great work ❤❤❤❤❤
What happen if the graph does not intersect with the y and x axis? How to graph the equation?
dear Andrew, the graph will always intersect at any point on y-axis. However, it it doesn't intersect x-axis, then NO real solutions!
Thanks for asking😀
Take care dear and all the best😃
Have a very happy and blessed New Year!
Thanks, good teaching😊
Very helpful! Thank you so much!
You are very welcome dear! I'm sure you are a brilliant and bright student 👍 I'm glad you liked it! Please keep sharing my channel with your family and friends. Take care dear and all the best😃
anyone know y=x^2 and y=-x^2+4, i thought when we reverse the sign of x it reflects in y-axis , but why this graph is reflecting in x-axis?, kindly clarify
My teacher doesn't taught me well on quadratic This is incredible.
Subscribed to your channel cox I learned something new😊😊😊
Thanks so much for this now i finally understand my teacher just yells at me when its him who is bad at explaining 😂 literally no one in my class understands so thank you sir
So nice of you dear. Please keep sharing premath channel
Thanks dear for the feedback. You are awesome 👍 Take care dear and stay blessed😃
Love and prayers from the USA!
thank you so much, fantastic explanatiin
Awesome explanations ✌️
Thanks sir this was really helpful
can I ask how to find the domain and range? thanks