SAT Math Advanced Math: Algebra Beyond Lines

Equivalent expression

An algebraic expression written in a different form but equal in value for every allowed input.

Domain

The set of input values for which an expression or function is defined.

Distributive property

The rule that multiplies a term across a sum or difference, such as a(b + c) = ab + ac.

Exponent rules

Laws for working with powers, such as a^m * a^n = a^(m+n), used only when any required restrictions are satisfied.

Difference of squares

A factoring pattern: a^2 - b^2 = (a - b)(a + b).

Perfect square trinomial

A trinomial that factors into a squared binomial, such as a^2 + 2ab + b^2 = (a + b)^2 or a^2 - 2ab + b^2 = (a - b)^2.

Rational expression

A fraction whose numerator and denominator are polynomials.

Completing the square

A method of rewriting a quadratic to create a perfect square trinomial, often to find vertex form.

Nonlinear equation

An equation whose graph is not a straight line, such as a quadratic, rational, or radical equation.

Quadratic equation

An equation of the form ax^2 + bx + c = 0, where a is not 0.

Quadratic formula

A formula for solving any quadratic equation: x = (-b ± sqrt(b^2 - 4ac)) / (2a).

Discriminant

The expression b^2 - 4ac, which tells how many real solutions a quadratic equation has.

Rational equation

An equation that contains rational expressions and must be solved while keeping denominator restrictions in mind.

Radical equation

An equation that contains a radical and is often solved by isolating the radical, squaring both sides, and checking the result.

Extraneous solution

A value produced during solving that does not actually satisfy the original equation.

Nonlinear system

A system of equations in which at least one equation is nonlinear.

Substitution

A method for solving a system by replacing one variable with an equivalent expression from another equation.

Nonlinear function

A function whose graph is not a straight line.

Quadratic function

A function of the form f(x) = ax^2 + bx + c whose graph is a parabola.

Standard form

The quadratic form f(x) = ax^2 + bx + c, which makes the y-intercept easy to identify.

Factored form

The quadratic form a(x - r1)(x - r2), which makes the zeros or x-intercepts easy to read.

Vertex form

The quadratic form a(x - h)^2 + k, which shows the vertex at (h, k).

Polynomial

An expression made of terms like a_n x^n where the exponents are nonnegative integers.

Rational function

A function written as p(x) / q(x); values that make q(x) = 0 are excluded from the domain and may create asymptotes or holes.

Radical function

A function that contains a radical, such as sqrt(x - 3), with a domain limited by the value inside the radical.