Formula sheet · Grades 9 to 11

Algebra 2 formulas

13 formulas from this course. Each one gives the rule in math, one line on what it means, and a worked example that uses it.

Quadratic formula

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

Solves every quadratic equation written as ax squared plus bx plus c equals zero.

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

Add half the middle coefficient squared to turn the left side into a perfect square.

x^2 = k \Rightarrow x = \pm\sqrt{k}

Isolate the square, then take the positive and negative roots.

D = b^2 - 4ac

A positive D gives two real roots, zero gives one, and a negative D gives no real roots.

a^2 - b^2 = (a - b)(a + b)

A square minus a square factors into a conjugate pair.

a^2 \pm 2ab + b^2 = (a \pm b)^2

When the middle term is twice the product of the square roots, the trinomial is one bracket squared.

ab = 0 \Rightarrow a = 0 \text{ or } b = 0

Set each factor to zero to find every solution of a factored equation.

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

Pair the terms, factor each pair, then take out the shared bracket.

(x^m)^n = x^{mn}

Raise a power to a power by multiplying the exponents.

x^{m/n} = \sqrt[n]{x^m}

The denominator of the exponent is the root and the numerator is the power.

\sqrt{a^2 b} = a\sqrt{b}

Pull the largest perfect square out of the radicand and leave the rest under the root.

\sqrt[3]{x} = k \Rightarrow x = k^3

Cube both sides to undo the cube root; no plus-or-minus sign is needed.

\sqrt{x} = k \Rightarrow x = k^2

Square both sides to remove the root, then check for false solutions.

Practice problems with answers for every Algebra 2 topic.