Topic 01

Algebra

Variables, equations, and functions. Learn to manipulate expressions, solve for unknowns, and understand how quantities relate to each other.

Visual Reference
Key Diagrams
Quadratic Function y = ax² + bx + c
vertex (h,k) x₁ x₂ y = ax² + bx + c x y
Linear Function y = mx + b
run rise b m = rise / run x y
Exponent & Power Rules
aˣ · aʸ = aˣ⁺ʸ (aˣ)ʸ = aˣʸ a⁻ⁿ = 1 / aⁿ a⁰ = 1
Reference
Core Formulas
Quadratic Formula
x = (−b ± √(b²−4ac)) / 2a
Solves ax² + bx + c = 0. The discriminant b²−4ac tells you how many real roots exist.
Slope-Intercept
y = mx + b
m = slope (rise/run), b = y-intercept where the line crosses the y-axis.
Point-Slope Form
y − y₁ = m(x − x₁)
Use when you know a point (x₁, y₁) and the slope m.
Difference of Squares
a² − b² = (a+b)(a−b)
A key factoring identity — recognizing this pattern saves a lot of steps.
FOIL
(a+b)(c+d) = ac+ad+bc+bd
First, Outer, Inner, Last — for expanding two binomials.
Vertex Form
y = a(x−h)² + k
The vertex of the parabola is at point (h, k).
Practice
Test Your Knowledge
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