Ex: Find the Equation of a Quadratic Function from a Graph

Ex:  Find the Equation of a Quadratic Function from a Graph


– WE WANT TO DETERMINE
THE EQUATION OF THE QUADRATIC FUNCTION
FROM THE GRAPH. WE ALSO WANT TO GIVE
THE FUNCTION IN GENERAL FORM. REMEMBER GENERAL FORM
OF A QUADRATIC FUNCTION IS F OF X=AX/SQUARED
+ BX + C. BUT TO FIND THIS FORM
OF THE FUNCTION, WE’RE ACTUALLY GOING TO USE
THE STANDARD FORM FIRST, WHICH IS F OF X=”A” x THE
QUANTITY X – H/SQUARED + K. SO THE FIRST THING WE’LL DO
IS REPLACE F OF X WITH Y SO WE’LL HAVE Y=”A” x THE
QUANTITY X – H/SQUARED + K. SO IN THIS FORM, HK WOULD BE
THE COORDINATES OF THE VERTEX AND XY WOULD REPRESENT
SOME POINT ON THE GRAPH. SO NOW LET’S TAKE A LOOK
AT OUR GRAPH. THIS WOULD BE OUR VERTEX. NOTICE HOW THE VERTEX WOULD
HAVE AN X COORDINATE OF -3 AND A Y COORDINATE OF +4. AND THEN NOTICE THIS POINT
HERE ON THE FUNCTION WOULD HAVE AN X COORDINATE OF
-4 AND A Y COORDINATE OF +2. THIS IS ACTUALLY
ALL THE INFORMATION WE NEED TO GET STARTED. SINCE THIS POINT IS
THE VERTEX, H=-3 AND K=+4 AND SINCE THIS POINT
IS ON THE FUNCTION WE CAN USE X=-4 AND Y=+2. SO AGAIN FROM HERE WE’RE GOING
TO SUBSTITUTE -3 FOR H, +4 FOR K, -4 FOR X,
AND +2 FOR Y. NOTICE WHEN WE DO THIS WE’LL
BE LEFT WITH ONE UNKNOWN, “A”. ONCE WE DETERMINE THE VALUE
OF “A” WE’LL HAVE THE FUNCTION
IN STANDARD FORM WHICH WE’LL THEN WRITE
IN GENERAL FORM. SO WERE GOING TO HAVE 2=”A”
x THE QUANTITY X – H, WELL X IS -4 – H
IS GOING TO BE – -3. AND WE’RE GOING TO SQUARE THIS
AND THEN ADD K AND K IS +4. SO NOW LET’S GO AHEAD
AND SIMPLIFY THIS. WE’LL HAVE 2=”A” x THIS
IS GOING TO BE -4 + 3 OR -1/SQUARED + 4. SO WE’LL HAVE 2=-1/SQUARED
IS JUST 1 SO 1 x “A” IS “A” + 4. SUBTRACT 4 ON BOTH SIDES
OF THE EQUATION. THIS IS 0.
SO WE HAVE -2=”A”. SO OUR FUNCTION
IN STANDARD FORM IS GOING TO BE F OF X=”A”
WHICH IS -2 AND THEN WE’LL HAVE
THE QUANTITY X – H/SQUARED. REMEMBER WE DO WANT X
IN OUR FUNCTION SO WE’RE GOING TO HAVE X – H,
BUT H IS -3, – -3 WILL BE +3. SO WE HAVE X – 3/SQUARED
AND THEN + K. AGAIN K IS 4, SO WE HAVE + 4. BUT SINCE WE WANT THIS
IN GENERAL FORM WE’LL HAVE TO MULTIPLY
THIS OUT, COMBINE LIKE TERMS AND THEN PUT THE TERMS
IN DESCENDING ORDER SO IT’S IN GENERAL FORM. SO LET’S DO THAT
ON THE NEXT SLIDE. SO WE’LL START BY SQUARING
THE QUANTITY X + 3. REMEMBER THERE ARE
NO SHORTCUTS. WE’LL HAVE TO WRITE THAT OUT
AS TWO FACTORS AND THEN MULTIPLY
THE TWO BINOMIALS. SO WE’LL HAVE FOUR PRODUCTS. 1, 2, 3, AND 4. SO I HAVE -2 x THIS PRODUCT
WHICH WILL BE X/SQUARED. THEN WE’LL HAVE + 3X + 3X,
THAT’S + 6X + 9 + 4. NOW WE’LL DISTRIBUTE THE -2. SO WE’LL HAVE
-2X/SQUARED – 12X – 18 + 4 AND WE HAVE TWO LIKE TERMS
HERE THAT WE CAN COMBINE. SO THE FUNCTION
IN GENERAL FORM WOULD BE F OF X=-2X/SQUARED – 12X AND THEN -18 + 4 IS GOING
TO BE -14 SO WE HAVE – 14. SO THIS WOULD BE THE GENERAL
FORM OF OUR QUADRATIC FUNCTION GIVEN BY THIS GRAPH. I HOPE YOU FOUND THIS HELPFUL.

100 thoughts on “Ex: Find the Equation of a Quadratic Function from a Graph

  • October 23, 2016 at 10:09 pm
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    i love you so much bro that was helpful very much

    Reply
  • November 10, 2016 at 8:03 pm
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    Thanks a mil

    Reply
  • November 10, 2016 at 10:24 pm
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    YOU SAVED ME THANK YOU I LOVE YOU

    Reply
  • December 5, 2016 at 1:07 am
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    thank you

    Reply
  • December 7, 2016 at 11:12 am
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    Life saver thank you

    Reply
  • December 13, 2016 at 5:23 am
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    big help thank you

    Reply
  • January 1, 2017 at 12:06 am
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    life saver..omg I fucking love uuu

    Reply
  • January 1, 2017 at 12:20 pm
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    I. LOVE. YOU <3

    Reply
  • January 16, 2017 at 7:36 pm
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    TY!

    Reply
  • January 18, 2017 at 7:43 pm
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    Thank you for this great explanation- very much appreciated-

    Reply
  • January 29, 2017 at 8:07 pm
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    So this whole time I've been looking through math forums trying to understand this o_o
    This video helped me sooo much!! Thank you

    Reply
  • March 5, 2017 at 11:18 am
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    Wow love this video! Really clear and easy to follow.

    Reply
  • March 11, 2017 at 6:55 pm
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    Hi, I noticed you didn't answer this one like all the other transformed functions. I used g(x)=af(b(x+c))+d and subbed in everything and got an equation that works. It's a little ugly but works. Why did you change it up on the parabola?

    Reply
  • March 13, 2017 at 4:43 pm
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    Thanks

    Reply
  • March 29, 2017 at 4:53 pm
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    Very helpful👌🏾

    Reply
  • April 24, 2017 at 4:49 am
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    Thank you

    Reply
  • May 4, 2017 at 4:47 pm
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    I was wondering how you would determine the equation of a graph if you only had a point on the graph and the x-intercept

    Reply
  • May 4, 2017 at 8:11 pm
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    Thanks i guess

    Reply
  • June 9, 2017 at 5:34 pm
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    Ty

    Reply
  • June 22, 2017 at 10:29 am
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    this is why i hate math soooo much. im literally doing my unwritten assignment right now. and i didnt understand anything in class today. ugh!!!!!

    Reply
  • September 19, 2017 at 4:56 pm
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    Quick and EASY!!! Thank you!

    Reply
  • November 21, 2017 at 9:58 pm
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    you saved me on my project

    Reply
  • December 2, 2017 at 7:06 am
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    Thank you so much man.

    Reply
  • December 12, 2017 at 4:58 am
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    Thank you this helped alot

    Reply
  • December 16, 2017 at 5:30 pm
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    Thanks, and everyone the x and y points are from another point besides the vertex that you WILL be given to determine that function.

    Reply
  • December 22, 2017 at 2:35 pm
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    Thank you wise man.

    Reply
  • January 19, 2018 at 3:10 pm
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    My teacher made it so hard to learn this, you helped me allot thank you

    Reply
  • January 25, 2018 at 3:51 am
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    thank you

    Reply
  • January 25, 2018 at 11:40 am
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    why was -3 converted to +3?

    Reply
  • January 30, 2018 at 12:48 pm
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    2 divided by negative four is negative one half not negative 2

    Reply
  • February 2, 2018 at 7:37 pm
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    fuCHitive

    Reply
  • February 10, 2018 at 9:26 pm
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    Thank you so much

    Reply
  • February 17, 2018 at 7:29 pm
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    I have a question….. What if they dont give the value of h

    Reply
  • March 7, 2018 at 2:54 am
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    What if the vertex is (0,0)

    Reply
  • March 10, 2018 at 7:20 pm
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    Thank you so much!! Great explanation

    Reply
  • April 9, 2018 at 11:23 pm
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    Why -h? Why not +h at the beginning?

    Reply
  • April 9, 2018 at 11:26 pm
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    What if the vertex is 0,5 and the parabola is going upward?

    Reply
  • April 10, 2018 at 4:41 pm
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    Who's here for GCSE's?

    Reply
  • April 14, 2018 at 2:26 pm
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    you are the best

    Reply
  • April 17, 2018 at 1:52 am
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    The Instructions were very clear, helpful and fabulous!! Thanks you sir!! You made day!! 🙂

    Reply
  • April 29, 2018 at 11:16 pm
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    bless you 🙏

    Reply
  • May 5, 2018 at 9:39 am
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    Will they give you the formula for general and standard form on the exam?

    Reply
  • May 24, 2018 at 7:45 pm
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    Hello, how can I contact with you? I’m having trouble with a problem similar to this

    Reply
  • June 12, 2018 at 1:32 am
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    lifesaver. Thank you!

    Reply
  • August 29, 2018 at 10:22 am
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    So you just pick a random point for x and y and then you're good?(good to go for solving)

    Reply
  • September 10, 2018 at 8:48 pm
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    Thank you so much :((

    Reply
  • September 18, 2018 at 2:53 pm
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    THANKS A BUNCH

    Reply
  • September 19, 2018 at 3:35 pm
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    The video is pretty helpful and will most probably help me on the rest of the stuff on math. Coincidentally, the example you used is apparently one of the questions on my assignment

    Reply
  • September 22, 2018 at 3:52 am
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    just what i was looking for ! thankyou !

    Reply
  • September 23, 2018 at 10:51 pm
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    Thank you! 😀

    Reply
  • September 30, 2018 at 11:51 pm
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    I wish my teacher could teach this clearly.

    Reply
  • October 8, 2018 at 1:29 pm
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    clutch

    Reply
  • October 22, 2018 at 7:59 am
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    Thankyou

    Reply
  • October 22, 2018 at 5:19 pm
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    I'm here because I don't wanna fail my exam lol

    Reply
  • October 29, 2018 at 10:27 am
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    Thanks man.

    Reply
  • November 22, 2018 at 12:55 am
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    I don't know if I'm just missing something but every other resource I have seen says that STANDARD form is f(x)=ax^2 +bx+c, and that VERTEX or TRANSFORMATION form is f(x)=a(x-h)^2 +k.

    Reply
  • December 9, 2018 at 6:52 am
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    sir is it possible a quadratic function have not parabola shape (y=-x2+6x-9)

    Reply
  • January 20, 2019 at 6:30 pm
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    which software you use????

    Reply
  • January 22, 2019 at 2:30 am
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    You saved my life too omg thank you

    Reply
  • February 22, 2019 at 12:53 am
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    thank youuu soo much

    Reply
  • February 28, 2019 at 2:04 am
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    You are a life saver

    Reply
  • March 4, 2019 at 12:09 am
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    What is h?

    Reply
  • March 15, 2019 at 6:03 pm
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    This is SO MUCH CLEARER than my professor and textbook. It's like classes are designed for students to fail.

    Reply
  • March 20, 2019 at 1:22 am
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    Omg thank you. I had all these other ways and I knew there was an easier way. Thank you!

    Reply
  • March 20, 2019 at 1:53 am
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    Isn’t there a shorter way of doing this

    Reply
  • March 22, 2019 at 1:39 am
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    i failed my algebra test bc of this

    Reply
  • March 27, 2019 at 6:43 am
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    you r really great,it helped me very much to understand calculous

    Reply
  • March 31, 2019 at 8:15 pm
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    Dude this helped so much with my homework dude👍👍👏

    Reply
  • April 14, 2019 at 12:40 am
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    THANK

    Reply
  • April 15, 2019 at 10:46 pm
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    I've been in algebra 1 honors for a year and this is the first time i've understood this concept completely. Thank you so much!!

    Reply
  • April 18, 2019 at 10:30 pm
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    Thank you so much!! 🧐👌👏

    Reply
  • May 12, 2019 at 6:33 pm
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    tysm ❤️❤️❤️

    Reply
  • May 13, 2019 at 11:05 pm
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    So difficult I need Help
    by the way I'm a freshman in high school taking Honors Algebra 1

    Reply
  • May 27, 2019 at 2:42 am
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    When putting it in standard form why don’t you use the general form value for x?

    Reply
  • May 29, 2019 at 4:59 pm
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    Thanks!

    Reply
  • July 5, 2019 at 2:03 am
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    Why dont teachers teach in such a clear concise, and efficient way? I tell you why… EDUCATION IS A MAFIA BUSINESS. Trying to prolong a 
    5-minute lecture for excruciating number of weeks so they can have full time jobs.

    Reply
  • August 13, 2019 at 11:29 am
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    Thank goodness a teacher who can finally save me from Math exams

    Reply
  • September 5, 2019 at 11:58 pm
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    we havent even learned this, and i already get it because of you, thank u

    Reply
  • September 12, 2019 at 11:40 am
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    Now I get this lesson but there seems to be another problem for me, what if the function does not have 0 in the table of values? So that means that the vertex is 2 points away from each other, how do I solve this?

    Reply
  • September 14, 2019 at 8:53 am
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    when i put this into a graphing calculator it just says error…

    Reply
  • September 17, 2019 at 9:03 pm
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    I am saved

    Reply
  • September 20, 2019 at 12:14 am
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    Bro you are a lifesaver

    Reply
  • September 20, 2019 at 9:37 am
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    Nicely done and explained.

    Reply
  • October 2, 2019 at 10:02 pm
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    Crying 😭

    Reply
  • October 9, 2019 at 2:50 pm
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    At 3:43 did he use FOIL?

    Reply
  • October 12, 2019 at 6:24 am
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    I just wanted to drop a comment and say you're an amazing teacher and you have helped me study for so many math exams thank you so much for doing these videos.

    Reply
  • October 16, 2019 at 11:14 pm
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    Where did the (-1)^2 go? I am confuse

    Reply
  • October 17, 2019 at 2:43 pm
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    Thank you

    Reply
  • October 31, 2019 at 6:04 am
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    Awesome explanation 🙂

    Reply
  • November 1, 2019 at 12:14 pm
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    could you simplify the final equation?

    Reply
  • November 10, 2019 at 4:38 am
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    thank youuuu :))))

    Reply
  • November 12, 2019 at 10:01 pm
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    Good job!

    Reply
  • November 14, 2019 at 4:17 am
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    I’m not sure if I understood it because it’s just one of those topics you just get, or because you showed it very clear and simple

    Reply
  • November 20, 2019 at 2:24 pm
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    This guy is only okay because he did not give me all my answers. i only got 99/100. he sucks

    Reply
  • November 20, 2019 at 2:30 pm
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    thisvideo dosent help much

    Reply
  • November 20, 2019 at 3:08 pm
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    itnstill takes forevr to do it

    Reply
  • November 22, 2019 at 2:59 am
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    How old is everyone here

    Reply
  • November 25, 2019 at 6:18 am
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    wow this makes it so much easier! thanks so much for that lil tutorial 🙂

    Reply
  • November 25, 2019 at 9:40 am
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    How do you get x and y?

    Reply
  • December 19, 2019 at 3:31 am
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    This 5 minute video really taught me more than my teacher did in 3 months. Thank you mate.

    Reply

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