# Parabola

Constructs a parabola. The general function of a parabola is $f\left(x\right)=a{x}^{2}+bx+c$, with $a\ne 0$; or, completing the square, $f\left(x\right)=a{\left(x+\frac{b}{2a}\right)}^{2}+\frac{4ac-{b}^{2}}{4a}$

## Syntax

```parabola(Real, Point, Vector)
```
```parabola(Real, Point)
```
```parabola(Real, Vector)
```
```parabola(Real)
```

## Description

Given a real $p$, a point $V$ and a vector $v$, constructs a parabola with focal semidistance equal to $p$, vertex at point $V$ and direction given by $v$.

Given a real $p$ and a point $V$, constructs a parabola with focal semidistance equal to $p$, vertex at point $V$ and direction given by $\left[0,1\right]$.

Given a real $p$ and a vector $v$, constructs a parabola with focal semidistance equal to $p$, vertex at the origin and direction given by $v$.

Given a real $p$, constructs a parabola with focal semidistance equal to $p$, vertex at the origin and direction given by $\left[0,1\right]$.