Conics - Parabola

What You'll Learn

Identify and graph vertical parabolas using transformations and vertex form

Recognize and sketch horizontal parabolas from equations with squared y-terms

Convert quadratic equations from general form to vertex form by completing the square

Locate the vertex, axis of symmetry, focus, and directrix of any parabola

Apply the conics formula p = 1/(4a) to find focus and directrix distances

Understand parabolas as curves equidistant from focus and directrix

What You'll Practice

Graphing vertical and horizontal parabolas with various transformations

Completing the square to convert equations to vertex form

Finding vertex coordinates by setting brackets equal to zero

Calculating focus and directrix using the parabola conics formula

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 square Shortcut: Vertex formula Graphing parabolas for given quadratic functions

This Unit Includes

7 Video lessons

Practice exercises

Skills

Parabolas

Vertex Form

Completing the Square

Conics

Focus and Directrix

Transformations

Axis of Symmetry

Quadratic Functions

OH Curriculum Aligned