Definition: The difference of cubes formula states that a³-b³ = $a-b$$a²+ab+b²$

Example: The equation of a circle in standard form is $x-h$² + $y-k$² = r², where (h,k) is the center and r is the radius

Highlight: Polynomial functions can be written in factored form as f(x) = a(x−p)(x−q)(x−r) where p, q, and r are the roots

Vocabulary: A fractional exponent can be converted to a radical form, where a^$1/n$ = ⁿ√a

Definition: Compound interest formula: A = P$1 + r$ⁿ, where A is final amount, P is principal, r is interest rate, and n is number of periods

Example: For continuous compound interest, the formula A = Pe^(rt) is used, where e is Euler's number

Highlight: The half-life formula N(t) = N₀(1/2)^$t/t₁/₂$ is crucial in radioactive decay calculations

Vocabulary: Asymptotes are lines that a curve approaches but never touches, defined by x = h and y = k in hyperbolic functions

Definition: The law of cosines states that a² = b² + c² - 2bc cos(A) for any triangle

Example: The area of any triangle can be calculated using A = de sin(f), where d and e are sides and f is the included angle

Highlight: Permutations $P(n,r) = n!/(n-r)!$ calculate arrangements where order matters

Vocabulary: The law of sines relates side lengths to angles: sin(A)/a = sin(B)/b = sin(C)/c

Definition: The probability formula for multiple selections involves combinations and specific conditions

Example: Vertical shifts in trigonometric functions are represented by adding or subtracting constants

Highlight: The tangent function V = tan(θ) relates to the ratio of sine and cosine

Vocabulary: Probability calculations often involve combinations $C(n,r) = n!/(r!(n-r)!)$ for selecting items where order doesn't matter

Definition: The quadratic formula is used to find the roots of any quadratic equation: x = $-b ± √(b² - 4ac)$/2a

Example: To find the axis of symmetry of a parabola, use the formula -b/2a

Highlight: The vertex form of a quadratic equation, f(x) = a(bx – h) + k, is particularly useful for graphing parabolas and finding maximum/minimum points

Vocabulary: Slope-intercept form $y = mx + b$ represents a linear equation where 'm' is the slope and 'b' is the y-intercept