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Algebra Formulas

Essential algebraic formulas including quadratic equations, logarithms, and polynomial expressions.

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

The universal solution for finding the roots of any quadratic equation of the form ax² + bx + c = 0.

m = \frac{y_2 - y_1}{x_2 - x_1}

Calculates the steepness or angle of a line between two points.

d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

Calculates the distance between two points in a 2D coordinate plane.

(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k

Expands the power of a binomial expression into a sum of terms involving binomial coefficients.

a_n = a_1 + (n-1)d

Finds the nth term of an arithmetic sequence (a progression where the difference between terms is constant).

a_n = a_1 \cdot r^{n-1}

Finds the nth term of a geometric sequence (progression by multiplication).

M = \left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)

Finds the midpoint between two points in a coordinate plane.

S_n = \frac{n}{2}(a_1 + a_n)

Calculates the sum of a finite arithmetic sequence.