![enter image description here](https://i.stack.imgur.com/G24jd.jpg)

A can be written as... $y = a$

B can be written as... $y = bx + a$

C can be written as... $y = cx^2 + bx + a$

1) How can I write D?
I was looking at implementing bezier curves into some code but is there something similar which could be computed much quicker?

2) C is a quadratic... what is the name for D?

Edit: ![enter image description here](https://i.stack.imgur.com/wUUuK.jpg)

Perhaps if I explain what I'm doing....
I am trying to build a decent servo controller.
I have a servo which will move from servo position 30 to 0. I want it to move in a more elegant way than B (above)... ideally like in the picture.
I will come up with a way of defining the movement between 2 positions when I send a command to the controller. Perhaps this is a quadratic equation which could be calculated easily for each x (time) between y (servo angles)... this would mean I would only need to pass a, b and c to the controller along with the time (length) and both positions.

I figured it would be better to have it able to be more irregular... but still super quick to compute. I considered bezier curves as a definition for the line, but they seem overcomplicated and slow to compute... if there anything else I could use?