A parabola is a curve with the parametric equations:
x = a t^2\\
y = 2 a t
$a$ is a positive constant, and
$t$ is the independent variable.
We can plot this curve by calculating the values of
$y$ for various values of
and drawing a smooth curve through them.
Curve for a = 1
$a = 1$, the parametric equations simplify to:
x = t^2\\
y = 2 t
The values are shown in the following table, for
$t$ in the range -3 to +3:
The animation below plots the points and then draw a curve through them. Press the Play button to show this: