Perhaps this questions was asked already, but I browsed through other threads and couldn't find exactly what I am looking for. I am looking for an Algebra Textbook (high-school/undergrad level) that teaches Algebra from the very fundamentals of math. This including proofs for how theorems were derived, use of inductive and deductive reasoning, how they quadratic formula was derived, etc. It would also help if the textbook covered geometric or graphical explanations. I have friends who have studied math in other countries, and they understand it much better than I do because in their countries, rather than just learning the theorems, they learned all the proofs and how the theorems were derived. Could someone please point out a textbook that does this? I would not mind if the textbook is really old, as I use textbooks decades old to try to learn math (e.g. Kiselev's Geometry, Spivak's Calculus).
This might be of interest to you. "Algebra" by I. Gelfand. He was a great mathematician who also brought his insights to write a text at the high-school level you want.
I think the book you're possibly looking for is Basic Mathematics by Lang.
Perhaps what you are looking for is one of the textbooks by Berkeley Professor H.H. Wu.
Although they are claimed to be directed at students (or teachers) at the pre-secondary level, you might still find what you seek: and, in any event, they are available for free through his homepage!
More generally, Wu's homepage.
I really like Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry by Simmons. It explores Algebra very well and has great examples.