The equation of a parabola in the form y² = 4px describes a parabola that opens to the right. Here, p represents the distance from the vertex to the focus of the parabola, which is a crucial parameter in defining its shape and position.
In the specific case of the equation y² = 4x, we can identify the value of p by comparing this equation to the general form. In y² = 4px, if we align 4px with 4x, we can determine that:
- 4p = 4
To find p, we simply divide both sides of the equation by 4:
- p = 1
Therefore, for the parabola described by the equation y² = 4x, the value of p is 1. This implication means that the distance from the vertex of the parabola to its focus is 1 unit. Understanding this value helps in graphing the parabola and determining its focus and directrix.