PSAT 10 Math — Advanced Algebra and Function Skills

Equivalent Expressions

Different-looking expressions that represent the same value for all allowed inputs.

Domain

The set of all possible inputs (values of the variable) for which an expression is defined.

Factor Out

To rewrite an expression by extracting the greatest common factor from its terms.

Combine Like Terms

The process of adding or subtracting terms that have the same variables raised to the same powers.

Distributive Property

Expands products by distributing one term across an addition inside parentheses.

Factored Form

An expression represented as a product of factors.

Vertex Form of a Quadratic

A quadratic function represented as $f(x)=a(x-h)^2+k$ where $(h,k)$ is the vertex.

Quadratic Formula

A formula used to find the roots of a quadratic equation: x=rac{-b ext{±} oot{b^2-4ac}}{2a}.

Discriminant

The expression $b^2-4ac$ under the square root in the quadratic formula that indicates the number of real solutions.

Absolute Value

The distance of a number from zero on the number line, denoted as $|x|$.

Radical Equation

An equation that involves a variable within a radical (square root) expression.

Rational Equation

An equation that involves a ratio of polynomials.

Intercepts

Points where a graph crosses the axis; x-intercepts where $y=0$ and y-intercepts where $x=0$.

Asymptotes

Lines that a graph approaches but never reaches, commonly found in rational functions.

Parent Function

The simplest function in a family of functions, used as a reference for transformations.

Transformations

Changes made to the parent function to produce a new function.

Exponential Growth

A situation where a quantity increases by a constant percentage over time.

Completing the Square

A method used to convert a quadratic expression into vertex form.

Max/Min Value

The highest or lowest point on the graph of a function, which occurs at the vertex for quadratic functions.

Function Notation

A way to write functions in the form $f(x)$ to indicate the output for input $x$.

Zero Product Property

If a product equals zero, at least one of the factors must equal zero.

Polynomial

An expression consisting of variables raised to non-negative integer powers and coefficients.

Radicand

The expression inside a radical sign.

Range

The set of all possible outputs (values of the function) for a given function.

System of Equations

A set of equations with the same variables, whose solutions satisfy all equations simultaneously.

Quadratic Equation

An equation of the form $ax^2 + bx + c = 0$.