Algebra 2 Focus and Directrix Flashcards

What is the formula for a parabola?

What is the vertex of a parabola in coordinate form?

What are the coordinates of the focus of a parabola?

What is the equation of the directrix of a parabola?

What is the axis of symmetry of a parabola?

The focus and the axis of symmetry of a parabola have different y-values.

On a parabola, the focus and directrix are at equal distances from the points on the graph.

Parabola Components

Formula for a Parabola: Represents the standard form, given by ((x-h)² = 4p(y-k)), where (p) indicates the distance from the vertex to the focus.
Vertex: The point where the parabola changes direction, represented by the coordinates ((h, k)).

Focus and Directrix

Focus: A specific point inside the parabola, denoted as ((h, k+p)), which affects the shape and orientation of the curve.
Directrix: A straight line given by (y = k-p) that is used to define the parabola alongside the focus.

Symmetry and Relationships

Axis of Symmetry: The vertical line that passes through the vertex, represented by (x = h), indicating the line of symmetry in the parabola.
Focus and Axis of Symmetry Relationship: The focus lies directly along the axis of symmetry, maintaining the same (y)-coordinate as the vertex.
Focus and Directrix Distance: Any point on the parabola is equidistant from both the focus and the directrix, emphasizing the definition of a parabola.

Enhance your understanding of the focus and directrix in conic sections with these Algebra 2 flashcards. Each card explains key terms and formulas, providing a quick reference for students. Brush up on essential concepts like vertex, axis of symmetry, and more.