Parabolas

These flashcards cover essential vocabulary related to parabolas, their definitions, and characteristics.

Parabola

The set of all points in a plane that are the same distance from a given point called the focus and a given line called the directrix.

Latus Rectum

The line segment through the focus of a parabola and perpendicular to the axis of symmetry.

Vertex

The point where the parabola changes direction; the midpoint between the focus and directrix.

Axis of Symmetry

The vertical line that passes through the vertex of a parabola, dividing it into two mirror-image halves.

Standard Form of a Parabola

The form of a parabola's equation written as y = a(x-h)² + k, where (h,k) is the vertex.

Direction of Opening

Determines whether the parabola opens upwards or downwards (for vertical parabolas) or right or left (for horizontal parabolas).

Directrix

A fixed line used in the definition of a parabola, such that any point on the parabola is equidistant from the focus and the directrix.

Focus

A specific point inside a parabola where rays that are parallel to the axis of symmetry converge.

Width of a Parabola

Determines how wide or narrow the parabola appears on a graph, often influenced by the coefficient 'a'.

Completing the Square

A method used to convert a quadratic equation into vertex form by reformulating it to express it as a perfect square trinomial.