Algebra 2 Honors - Formulas for Finals

log_b(x) = y ↔ b^y = x

Logarithmic ↔ Exponential form conversion

log_b(xy) = log_b(x) + log_b(y)

Log product rule

log_b(x/y) = log_b(x) - log_b(y)

Log quotient rule

log_b(x^r) = r log_b(x)

Log power rule

y = a * b^t or y = a * e^(kt)

Exponential growth/decay models

a_n = a₁ + (n - 1)d

Arithmetic sequence formula

S_n = (n/2)(a₁ + a_n)

Sum of an arithmetic series

a_n = a₁ * r^(n-1)

Geometric sequence formula

S_n = a₁ * (1 - rⁿ)/(1 - r)

Sum of a finite geometric series (r ≠ 1)

S_∞ = a₁ / (1 - r)

Sum of an infinite geometric series (|r| < 1)

a₁ = value, an = a_n-1 + d

Recursive arithmetic formula

a₁ = value, an = a_n-1 * r

Recursive geometric formula

∑_{i=1}^{n} f(i)

Sigma notation meaning

P(E) = favorable / total outcomes

Basic probability formula

P(A and B) = P(A) * P(B)

Probability of two independent events

P(A or B) = P(A) + P(B) - P(A and B)

General 'or' rule

P(B|A) = P(A and B) / P(A)

Conditional probability

_nP_r = n! / (n - r)!

Permutations (order matters)

_nC_r = n! / (r!(n - r)!)

Combinations (order doesn't matter)

P(k) = C(n, k) * p^k * (1 - p)^(n-k)

Binomial probability formula

E = Σ(value * probability)

Expected value formula

(x - h)² + (y - k)² = r²

Circle equation

((x - h)²)/a² + ((y - k)²)/b² = 1

Ellipse equation

c² = a² - b²

Distance to foci in ellipse

((x - h)²)/a² - ((y - k)²)/b² = 1

Hyperbola equation (horizontal)

c² = a² + b²

Distance to foci in hyperbola

y - k = ±(b/a)(x - h)

Asymptotes (horizontal hyperbola)

(x - h)² = 4p(y - k)

Vertical parabola equation

(y - k)² = 4p(x - h)

Horizontal parabola equation