Algebra 2 Toolkit: Formulas & Concepts

A comprehensive cheat sheet covering essential Algebra 2 topics including quadratic equations, logarithms, exponential functions, transformations, and basic trigonometry.

Core Principles

Quadratic Formula: Solves for roots of ax²+bx+c=0 using x = [-b ± sqrt(b²-4ac)] / 2a.
Logarithm Properties: Understand base conversions (log₁₀=log, logₑ=ln) and change of base formula (log_b(a) = log(a)/log(b)).
Exponential Growth/Decay: Modeled by y = a(1+r)ᵗ (compounded annually) or y = aeʳᵗ (compounded continuously).
Function Transformations: Shifts (±h, ±k), stretches (a·f(bx)), and reflections (-f(x), f(-x)) alter parent functions.
Trigonometric Ratios: SOH CAH TOA defines sin, cos, tan using opposite, adjacent, and hypotenuse.
Pythagorean Theorem: In a right triangle, a² + b² = c², where c is the hypotenuse.

Formulas

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$
$y = a(1+r)^t$
$y = ae^{rt}$
$g(x) = a \cdot f(b(x-h)) + k$
$a^2 + b^2 = c^2$
$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
$a^2 = b^2 + c^2 - 2bc \cos A$

People

Unknown Author: Compiler of Toolkit
Ms. Young: Teacher mentioned in statistical examples
Tucker: Investor in financial example