In Exercises 73-82, find the standard form of the equation of the parabola with the given charac

step 1 this is a problem number 80 vertex is minus 2 .1 which is h comma k and directrix is x equal to

In Exercises 73-82, find the standard form of the equation...

Key Concepts

Vertex

The vertex is the point on the parabola that is exactly midway between the focus and the directrix. It serves as the turning point of the curve and is used as the reference point in the standard equation of a parabola, determining its position on the coordinate plane.

Distance Parameter (p)

The parameter p indicates the distance between the vertex and the focus (and equivalently, to the directrix) in a parabola. Its magnitude determines how 'wide' or 'narrow' the parabola is, while its sign indicates the direction in which the parabola opens relative to the vertex.

Standard Form Equation

The standard form equation of a parabola involves writing the relationship between the coordinates of points on the parabola and its vertex, focus, and directrix. Depending on whether the parabola opens horizontally or vertically, the equation typically appears as (x-h)² = 4p(y-k) for vertical parabolas or (y-k)² = 4p(x-h) for horizontal parabolas, where (h, k) is the vertex and p is the distance from the vertex to the focus.

Parabola

A parabola is a conic section defined as the set of all points that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix). This geometric definition leads to its characteristic U-shaped curve that can open upward, downward, left, or right depending on its orientation.

Directrix

The directrix is a fixed line that, along with the focus, defines a parabola. Every point on the parabola is at an equal distance from the focus and the directrix. The position of the directrix relative to the vertex helps determine the orientation and the opening direction of the parabola.

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