Quadratic Formula - Printable Version

Quadratic Formula - Printable Version

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Quadratic Formula - Hazzy - 2008-07-06

Most of us know the Quadratic Formula and how to use it, but does anyone know where it came from?

I'm trying to Google, but not working well. D:

Quadratic Formula - Worthyness - 2008-07-06

From what i remember from my 9th grade summer, I believe you can derive the quadratic formula from ax^2+bx+c. However, i have forgotten that as of now... I am assuming the quadratic equation is :

x=-b+ or - (sqrt(b^2 - 4ac))/ 2a

I'm a bit rusty, it's summer afterall and i haven't used this since the beginning of calculus ><"

Edit:
Did you mean where did it come from as in country/civilization? because i can't help you there...
But if you want to derive the formula, use the completing the square method on the equation
ax^2+bx+c

Sorry if i can't be of any more use =O

Quadratic Formula - Hazzy - 2008-07-06

Worthyness Wrote:From what i remember from my 9th grade summer, I believe you can derive the quadratic formula from ax^2+bx+c. However, i have forgotten that as of now... I am assuming the quadratic equation is :

x=-b+ or - (sqrt(b^2 - 4ac))/ 2a

I'm a bit rusty, it's summer afterall and i haven't used this since the beginning of calculus ><"

Edit:
Did you mean where did it come from as in country/civilization? because i can't help you there...
But if you want to derive the formula, use the completing the square method on the equation
ax^2+bx+c

Sorry if i can't be of any more use =O

I meant how you connect the ax^2+bx+c=0 to the Formula. :/

Quadratic Formula - Worthyness - 2008-07-06

Let's see if i can do this right...

ax^2+bx+c=0
x^2 + b/a x = -c/a divide by "a"
x^2 + b/a x + ((1/2)(b/a x))^2 = -c/a + ((1/2)(b/a x))^2 completing the square
x^2 + b/a x + b^2/4a^2 = -c/a + b^2/4a^2 simplified
(x^2 + b/2a )^2 = -c/a + b^2/4a^2 Into binomial form (completed square)

x+ b/2a = sqrt(-c/a + b^2/4a^2 ) square root both sides
x= - b/2a + or - sqrt(-c/a + b^2/4a^2 ) move b/a x to other side

x= - b/2a + or - sqrt((-c/a * 4a/4a) + b^2/4a^2 ) common denominator

x= - b/2a + or - (sqrt( b^2 -4ac))/2a simplified

x= (- b + or - sqrt(b^2 - 4ac))/2a simplify more = quadratic formula.

hopefully you can read this... sorry if it is totally incoherent. but i believe that is how it is done... good luck with this =)

Quadratic Formula - x0xpriestx0x - 2008-07-08

here is a more clear answer to what you are looking for

http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html

Quadratic Formula - xCenario - 2008-07-09

I was going to post my answer but Worthyness has it right, ima make it easier for you guys Big Grin

Nvm it works now

Quadratic Formula - Hazzy - 2008-07-09

xCenario Wrote:I was going to post my answer but Worthyness has it right, ima make it easier for you guys

Can someone teach me how to put these images? >_> someone please put it

You did it right, Fiel just spilled some Chinchilla Bathing Powder on the server so those tags don't work right.

Also, thanks for the picture, my eyes don't ache from reading this one. XD

x0xpriestx0x, sorry, didn't see your post 'till just now. D: Thanks for the link. <3

Quadratic Formula - xCenario - 2008-07-10

By the way I use a program called TexnicCenter, with a codifier called Miktex.

This is called LaTeX, there is a tutorial on how to use this in http://www.artofproblemsolving.com where it says LaTeX in the left.

Quadratic Formula - Worthyness - 2008-07-10

Hazzy Wrote:Also, thanks for the picture, my eyes don't ache from reading this one. XD
<3

LOL sorry for that... i didn't know how to make it pretty Cool

Quadratic Formula - Thunda - 2008-07-10

I had an account on AoPS a long time ago...

Does anyone know who first derived that formula?

Quadratic Formula - xCenario - 2008-07-11

I dont know certainly who did it, but I wouldnt doubt it would be the Egyptians. Or Euclid, Pythagoras, or Diophantus.

Quadratic Formula - Worthyness - 2008-07-11

http://www.sosmath.com/algebra/factor/fac11/fac11.html

hope the link works...

Quadratic Formula - Trinity - 2008-07-11

that went way over my head ><