Explanation of origins of algebraic formulae

[Soonbethere]

EXPLAINING FORMULAE
Are there any books that explain why the terms of particular formulae are located in their positions ? For example, and just as an example, in the special formula for quadratic equations why is ‘a’ put below the line? Why is ‘a’ multiplied by ‘c’ ?
Are there any books that describe particular formulae and explain the reasons why the terms are located in their positions ?
Thank you.

 

[ksdhart]

Well, I can't speak for any specific textbook, as it's been far too long since I studied anything except Calculus. From what I do recall though, lower level textbooks don't tend to have good (or even any) explanations for how the formulas were derived. That said, you can always try searching the internet for the information. If you Google "deriving (name of formula)" or "proof of (name of formula)" you'll likely find a satisfactory explanation. In some cases though, the explanation/proof may be very difficult to understand because deriving the formula requires higher level math.

As for the quadratic formula, it arrives from working with the general form ax² + bx + c and completing the square. Googling "deriving the quadratic formula" returned this webpage, which has an excellent full explanation, as the first result: http://www.purplemath.com/modules/sqrquad2.htm

 

[Soonbethere]

Explanation of formulae -

Well, I can't speak for any specific textbook, as it's been far too long since I studied anything except Calculus. From what I do recall though, lower level textbooks don't tend to have good (or even any) explanations for how the formulas were derived. That said, you can always try searching the internet for the information. If you Google "deriving (name of formula)" or "proof of (name of formula)" you'll likely find a satisfactory explanation. In some cases though, the explanation/proof may be very difficult to understand because deriving the formula requires higher level math.

As for the quadratic formula, it arrives from working with the general form ax² + bx + c and completing the square. Googling "deriving the quadratic formula" returned this webpage, which has an excellent full explanation, as the first result: http://www.purplemath.com/modules/sqrquad2.htm

Thank you ksdhart that is really helpful. Regards.