Parabolas, Canonical form, help please..

Okay I wanna be clear, this is not an homework question.

But I have a hard time understanding the concept of what I'm gonna show you. The teacher goes way to fast for me, honestly, and when we ask a question it's just like he doesn't wanna take the time to make us understand, kinda makes me feel stupid.

So I'm writing me question with the hopes that you can point me a tutorial (hopefully video) or if you are good in the subject and can help me a little. I just want to grip the concept so I can have fun doing those because I'd understand...

**broken link removed**

I beleive there an equation that's like y = a (x - h)² + b
You know, I think I understand 80% of that factorization thing, but I have no clue about the parabola.

Things I'd like to know and remember:

- How to know if the parabola is pointing and how much is it "open" (I hope you understand what I mean).
- How to place the parabola at the good place (the - h thing lost me).
- The canonical form, what's the big deal ? Why can't it be simpler :|

I'm sorry if this is a stupid question but when I look at my notes it's all just whatever (the teacher goes so fast, I spend the time writing wh he writes on the chalkboard but I can't follow)

thank you

Hello,


You should probably look up basic properties of the parabola first, like the focus, etc.
Im not sure if you are interested in rotations or not.

Better than a tutorial or a video, just goof around with this thing for a few minutes -
https://www.mathwarehouse.com/quadratic/parabola/interactive-parabola.php