When defining hyperbolic trig functions, hyperbolic sector is involved, it is the area enclosed by the red and green curve and x-axis (see this desmos graph: Hyperbolic sector), so this inspires me to define parabolic sector, I define it as the area enclosed by the black and blue curve (see this desmos graph: Parabolic sector), so then I can establish a relationship between parabolic sector and x-y coordinate of a point on the parabola, or the expression for parabolic function.
Is this the correct way to define parabolic function? Does parabolic function exist at all? I saw this question on the site but I don't really understand the answer to it.
