Parabola example
Martin McBride
2020-09-12
- Categories:
- coordinate systems
- pure mathematics
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:
| t | x | y |
|---|---|---|
| -3 | 9 | -6 |
| -2 | 4 | -4 |
| -1 | 1 | -2 |
| 0 | 0 | 0 |
| 1 | 1 | 2 |
| 2 | 4 | 4 |
| 3 | 9 | 6 |
Here are the points plotted on a graph:
The curve can be drawn by plotting the points and drawing a smooth line through them:
