– 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.

Wow thank you so much! I just subscribed, your videos always help me!!

i love you so much bro that was helpful very much

Thanks a mil

YOU SAVED ME THANK YOU I LOVE YOU

thank you

Life saver thank you

big help thank you

life saver..omg I fucking love uuu

I. LOVE. YOU <3

TY!

Thank you for this great explanation- very much appreciated-

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

Wow love this video! Really clear and easy to follow.

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?

Thanks

Very helpful👌🏾

Thank you

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

Thanks i guess

Ty

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!!!!!

Quick and EASY!!! Thank you!

you saved me on my project

Thank you so much man.

Thank you this helped alot

Thanks, and everyone the x and y points are from another point besides the vertex that you WILL be given to determine that function.

Thank you wise man.

My teacher made it so hard to learn this, you helped me allot thank you

thank you

why was -3 converted to +3?

2 divided by negative four is negative one half not negative 2

fuCHitive

Thank you so much

I have a question….. What if they dont give the value of h

What if the vertex is (0,0)

Thank you so much!! Great explanation

Why -h? Why not +h at the beginning?

What if the vertex is 0,5 and the parabola is going upward?

Who's here for GCSE's?

you are the best

The Instructions were very clear, helpful and fabulous!! Thanks you sir!! You made day!! 🙂

bless you 🙏

Will they give you the formula for general and standard form on the exam?

Hello, how can I contact with you? I’m having trouble with a problem similar to this

lifesaver. Thank you!

So you just pick a random point for x and y and then you're good?(good to go for solving)

Thank you so much :((

THANKS A BUNCH

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

just what i was looking for ! thankyou !

Thank you! 😀

I wish my teacher could teach this clearly.

clutch

Thankyou

I'm here because I don't wanna fail my exam lol

Thanks man.

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.

sir is it possible a quadratic function have not parabola shape (y=-x2+6x-9)

which software you use????

You saved my life too omg thank you

thank youuu soo much

You are a life saver

What is h?

This is SO MUCH CLEARER than my professor and textbook. It's like classes are designed for students to fail.

Omg thank you. I had all these other ways and I knew there was an easier way. Thank you!

Isn’t there a shorter way of doing this

i failed my algebra test bc of this

you r really great,it helped me very much to understand calculous

Dude this helped so much with my homework dude👍👍👏

THANK

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!!

Thank you so much!! 🧐👌👏

tysm ❤️❤️❤️

So difficult I need Help

by the way I'm a freshman in high school taking Honors Algebra 1

When putting it in standard form why don’t you use the general form value for x?

Thanks!

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.

Thank goodness a teacher who can finally save me from Math exams

we havent even learned this, and i already get it because of you, thank u

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?

when i put this into a graphing calculator it just says error…

Bro you are a lifesaver

Nicely done and explained.

Crying 😭

At 3:43 did he use FOIL?

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.

Where did the (-1)^2 go? I am confuse

Thank you

Awesome explanation 🙂

could you simplify the final equation?

thank youuuu :))))

Good job!

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

This guy is only okay because he did not give me all my answers. i only got 99/100. he sucks

thisvideo dosent help much

itnstill takes forevr to do it

How old is everyone here

wow this makes it so much easier! thanks so much for that lil tutorial 🙂

How do you get x and y?

This 5 minute video really taught me more than my teacher did in 3 months. Thank you mate.