Pattern · Shape · Roots · General solution

Quadratic Equations

A five-lesson unit that connects quadratic tables, parabolic geometry, zero-output solutions, square construction, and the general solving formula.

Unit throughline

A quadratic is one relationship viewed through pattern, shape, and solution.

This page organizes the unit. The actual teaching lives in the lessons below, so each lesson can keep one primary question and one primary learning object.

detect the pattern → place the vertex → interpret roots → build a square → solve generally
01live
Quadratic Patterns & Parabolas
constant second Δ
02live
Vertex Form & Transformations
y = a(x − h)² + k
03live
Roots & X-Intercepts
f(r) = 0
04live
Completing the Square
x² + bx + (b/2)²
05live
Quadratic Formula & Discriminant
Δ = b² − 4ac
Lessons

Follow the sequence on a first pass. Planned lessons stay visible so the shape of the unit remains clear.

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