Of humbleness and understanding your domain

On New Year's Day, I felt really confident on my quest to learn Calculus. I would say over confident. Even after getting excellent advice on where to start (Pre Calculus), I pushed on with the Calculus books I had. Then I hit the wall. Yes, The Wall. The wall of realization that I was getting nowhere. The wall that has a sign that says:"if you are here and do not know what to do next, you missed a step, go back and return when ready."
Hitting that wall was (and still is) painful because of my pride.
 
Had I been humble, and realized I had not done math like this in a long time, I would have started from a math place I am still comfortable with. But no, I believed myself to be just a little fuzzy about quadratic equations and trigonometry. Oh, how wrong I was. How wrong was I? Would you like to know? Ok, let's give you an example of a phrase I found in the MIT Calculus for beginners page that baffled me.
 

The equation ax² + bx + c = 0 can be rewritten (when a is not 0, after dividing by a) as

That my friends is just an algebraic manipulation. A simple exercise in the grand scheme of things. Still, I could not follow the steps taken to get there. That was my wake up call. I need to go back to pre-calculus, back to functions, back to the last place I feel comfortable with.

That's how I landed in general function theory. I mean I work with functions all the time. How many calls have got in a weeks time? How much have we paid in cable over the last year? How much has our kilowatt hour fluctuated in 3 years? I love graphing things out, so I should start there, right?

Wrong.

Because when I tried starting with general function theory I ran into this gem in wikipedia when reviewing domains (which the course tells me is very important for pre-calculus and calculus problems)

For a function

defined by

, or equivalently ,

the codomain of f is , but f does not map to any negative number. Thus the image of f is the set ; i.e., the interval [0, ∞).

I must have stared at those statements for 5 minutes straight, before realizing that I had no idea what they meant. The English I got...but the symbols baffled me. After much rumination, and 6 hours of sleep, I went back to them and did what I should have done from the start. Went even further back to get the notations right.

Translation (as best I could come up with): , means for a function with a domain (the universe of numbers you will input into a function) of the Real Number (numbers that you can put on a graph) and a codomain (all the numbers the function could assumed as defined even when the function won't output all values in that codomain) that is also all Real numbers.

That translation took me an hour, and half a dozen websites to produce...but hey, that's progress.

Let me know if I am on the right track!