# 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: