Parabola example

A parabola is a curve with the parametric equations:

$$ \begin{align} x = a t^2\newline y = 2 a t \end{align} $$

Where $a$ is a positive constant, and $t$ is the independent variable.

We can plot this curve by calculating the values of $x$ and $y$ for various values of $t$, and drawing a smooth curve through them.

Curve for a = 1

Assuming $a = 1$, the parametric equations simplify to:

$$ \begin{align} x = t^2\newline y = 2 t \end{align} $$

The values are shown in the following table, for $t$ in the range -3 to +3:

Here are the points plotted on a graph:

The curve can be drawn by plotting the points and drawing a smooth line through them: