Algebra Formulas

Combining Like Terms

ax + bx = (a + b)x

Combining like terms merges coefficients of identical variables to simplify expressions and solve equations more efficiently.

FOIL Method

(a + b)(c + d) = ac + ad + bc + bd

The FOIL Method expands products of two binomials by multiplying each term in the first binomial by each term in the second.

Quadratic Formula

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

The Quadratic Formula solves any equation of the form ax^2 + bx + c = 0 in one step, giving both solutions at once without factoring.

Discriminant

\Delta = b^2 - 4ac

The discriminant, given by b^2 - 4ac, tells you whether a quadratic equation has real solutions and how many without actually solving it.

Completing the Square

x^2 + bx = \left(x + \frac{b}{2}\right)^2 - \frac{b^2}{4}

Completing the square rewrites a quadratic as a perfect square plus a constant, making it easier to solve and find the parabola's vertex.

Vertex Form

y = a(x - h)^2 + k

Vertex Form reveals a parabola's vertex and axis of symmetry at a glance, making it ideal for transformations and optimization problems.

Vertex of a Parabola

h = -\frac{b}{2a}, \quad k = c - \frac{b^2}{4a}

Find the lowest or highest point of a parabola using the vertex formula, which works for any quadratic equation in standard form.

Sum and Product of Roots

r_1 + r_2 = -\frac{b}{a}, \quad r_1 r_2 = \frac{c}{a}

Quickly find how a quadratic's roots add up and multiply together without solving for them — use when you need those relationships.

All 8 formulas in this topic