From parabolic purgatory to elliptical elation

It feels good when things make sense. When even just a tiny piece of the world is ordered, and you get that order.

I wasn't getting it.

By "it" I mean parabolas. You know, those U-shaped graphs. They look so innocent, don't they? Until you learn that you're to locate not only the graph's vertex (a simple task, really), but also its axis, focus, and directrix. My precalculus review book spelled it all out - all 10 formulas that I had to remember, depending on whether the parabola opened vertically or horizontally. But there was no explanation as to why these formulas existed. How were they derived? What did all those variables mean? 

Nothing. I was just expected to remember them. And to use them upon command.

Uh, yeah, right. Just call me a math monkey.

No. I need to understand why. To have things make sense in a larger way. But apparently my book's author wasn't interested in that. Or perhaps there was a budget cut and the book had to be shortened and that piece of instructional text cut out. Maybe. 

Not that it matters. Either way, I was on my own in my parabolic purgatory. I avoided math for a day or two. Then today I picked it up again. I looked at the graphs. I looked at the equations. I looked at the graphs again. And a light went on. 

"Ohhhhh .......... " The sound of relief. "So that's what "p" represents. I GET it now!"

With that one bit of knowledge - the meaning of "p" - I completely understood all 10 formulas, and rather than blindly memorizing them, was able to reason through them while completing (successfully) the practice set. 

Nearly dizzy with glee, I turned the page. Next topic: ellipses. And thought to myself, OK, they're just flattened circles, no big deal. But wait. There are two kinds of ellipses - horizontally squashed ones and vertically stretched ones. And for each, there are seven (for a total of 14) important points to remember. Plus two formulas. Plus the equation for finding "c." (Whatever "c" is ...) That's 17 things to remember, minimum!  And again, no explanation of how or why, no way to help me remember. Ack.

I could feel the pressure building up in my brain. A serious case of mathocephalus. 

I took a long draw on my espresso. I prayed for an ephiphany. But just as with parabolas, there would be no epiphany. There would only be hard work, there would be me reasoning things through and helping me help myself. 

I sighed and focused on the graphs. OK, this length represents "a," that's "b," the other one is "c," hold on, THIS MAKES SENSE! (It is math, after all.) 

Elation. But also a realization: I would probably have to do the same thing with the next page, and the page after that ... I would have to keep working through things. I was past the easy stuff. This required work. And sometimes work is frustrating. It is also rewarding, when you put the necessary time and effort into it.