Domain_02.1

INTEGRATED ALGEBRA

Simulation Deck

Slope Interceptor

y =1x+0

Slope (m) - The Angle1

Y-Intercept (b) - The Shift0

Origin (0,0)

Phase 1: Linear Realities

Algebra Fundamentals

The Language of Math

Real numbers, order of operations, properties of equality, and variable expressions.

Syntax3(x - 5) + 2

Graphing Linear Eq.

Lines & Slopes

Slope-intercept form, point-slope form, and graphing lines on a coordinate plane.

Syntaxy = -2x + 4

Systems of Equations

Intersection Points

Solving linear systems via graphing, substitution, and elimination methods.

Syntax{ 2x+y=10, x-y=2 }

Algebraic Inequalities

Shaded Regions

Solving and graphing single and compound inequalities.

Syntax-3x < 12

Phase 2: Curves & Powers

Quadratic Equations

Parabolas

Vertex form, standard form, quadratic formula, and completing the square.

Syntaxx = (-b±√Δ)/2a

Factoring

Reverse Multiplication

GCF, difference of squares, and trinomials decomposition.

Syntaxx² - 9 = (x-3)(x+3)

Exponents

Power Rules

Laws of exponents, scientific notation, and exponential growth/decay.

Syntax (x²)³ = x⁶

Radical Expressions

Roots & Exponents

Simplifying square roots, cube roots, and fractional exponents.

Syntax√(16x⁴) = 4x²

Phase 3: Abstractions

Functions

Input / Output

Domain, range, function notation f(x), and composite functions.

Syntaxf(g(x))

Rational Expressions

Algebraic Fractions

Simplifying, multiplying, and dividing fractions containing variables.

Syntax(x²-1)/(x+1)

Complex Numbers

The Imaginary Unit

Imaginary numbers, complex plane, and operations with complex numbers.

Syntaxi = √-1

Verification Protocol

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