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Advanced Algebra Through Visual Representation

Quadratic Functions

$$ f(x) = ax^2 + bx + c $$

a: 1 b: 0 c: 0

Step-by-Step Solution Revealer

Solving $$ ax^2 + bx + c = 0 $$

1. Identify coefficients: a = 1, b = 0, c = 0

2. Compute discriminant: $$ D = b^2 - 4ac $$

3. Apply quadratic formula: $$ x = \frac{-b \pm \sqrt{D}}{2a} $$

4. Simplify and solve for x

Polynomial Root Finder

Enter a cubic polynomial: $$ ax^3 + bx^2 + cx + d $$

Systems of Equations – Matrix Animation

Solving:

$$ \begin{cases} ax + by = e \\ cx + dy = f \end{cases} $$

Algebraic Identities – Area Model

Visualize: $$ (a + b)^2 = a^2 + 2ab + b^2 $$