Algebra 2 Toolkit Final

This cheat sheet covers essential Algebra 2 concepts including quadratic equations, logarithms, exponential functions, transformations, and basic trigonometry, providing formulas, rules, and examples for quick reference.

Core Principles

Quadratic Formula: Solves for the roots of a quadratic equation ax² + bx + c = 0 using $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$.
Logarithm Properties: Includes definitions like $log_b a = x \iff b^x = a$, and change of base formula $log_b a = \frac{log a}{log b}$.
Exponent Rules: Covers product, quotient, power rules, and rules for zero, negative, and fractional exponents.
Exponential Growth/Decay: Modeled by $y = a(1+r)^t$ for annual compounding and $y = ae^{rt}$ for continuous compounding.
Function Transformations: Understand how translations, reflections, and stretches/shrinks affect the parent function's equation.
Trigonometric Ratios: SOH CAH TOA helps find sides (Sin, Cos, Tan) and angles (Sin⁻¹, Cos⁻¹, Tan⁻¹) in right triangles.

Formulas

Quadratic Formula: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
Compounded Annually: $y = a(1+r)^t$
Compounded Continuously: $y = ae^{rt}$
Pythagorean Theorem: $c^2 = a^2 + b^2$
Law of Sines: $rac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
Law of Cosines: $a^2 = b^2 + c^2 - 2bc \cos A$

People

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