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Conics - Parabola

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Geometry
25. CC.HSG.GPE.A.2
25.1 Conics - Parabola

Conics - Parabola: Vertex, Focus, and Directrix

Understand the parabola as a conic section: its standard equation, vertex, axis of symmetry, focus, directrix, and latus rectum, explained step by step.

What You'll Learn

Define a parabola as the set of points equidistant from a fixed focus and a fixed directrix line.
Identify the standard form equations for parabolas opening upward, downward, leftward, or rightward.
Calculate the vertex, focus, and directrix from a parabola equation using the value of p.
Apply the axis of symmetry formula to locate the line that splits the parabola into mirror halves.
Measure the latus rectum as the chord through the focus perpendicular to the axis of symmetry.
Connect the conic definition of a parabola to the quadratic function vertex form you already know.

What You'll Practice

1

Graphing vertical and horizontal parabolas with various transformations

2

Completing the square to convert equations to vertex form

3

Finding vertex coordinates by setting brackets equal to zero

4

Calculating focus and directrix using the parabola conics formula

5

Determining opening direction from the sign and variable of the squared term

Why This Matters

Parabolas appear everywhere in real lifefrom satellite dishes that focus signals to a single point, to the paths of projectiles and the design of car headlights. Mastering parabola concepts gives you the tools to analyze these curved shapes mathematically and understand how focus and directrix properties make parabolic technology work in engineering and physics applications.

Before You Start — Make Sure You Can:

Quadratic function in vertex form: y = a(x-p)^2 + qConverting from general to vertex form by completing the squareShortcut: Vertex formulaGraphing parabolas for given quadratic functions

This Unit Includes

7 Video lessons
Practice exercises
Learning resources

Skills

Parabolas
Vertex Form
Completing the Square
Conics
Focus and Directrix
Transformations
Axis of Symmetry
Quadratic Functions
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