How do Quadratic Algebra work?

Question

Hello,

I would like to know how Quadratic Algebra actually works. I searched it on google but it’s so confusing…

For your information, my age is 11. I know up to intermediate algebra. I also know geometry and pretty advance fractions.

What I know is that Quadrant Algebra makes curved lines in a Cartesian Plane, while Linear Algebra (Which I know) makes straight lines on the Plane.

So can someone please tell me how it works?

(Maybe you can use this equation and explain it one by one):

2w² − 4w − 5 = 0

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Anyways, thanks for reading up to the end! I hope you’ll let me understand!