PSAT 8/9 Advanced Math: Expressions, Nonlinear Equations, and Nonlinear Functions

Expression

A mathematical phrase combining numbers, variables, and operations, e.g., $3x+7$.

Equivalent Expressions

Two expressions that have the same value for every allowed value of the variable(s).

Distributive Property

A property that states $a(b+c)=ab+ac$.

Factoring

The process of breaking down an expression into products of simpler expressions.

Combining Like Terms

The process of adding or subtracting terms with the same variable part.

Exponent Rules

Rules that govern the operations on exponents, such as multiplying and dividing same bases.

Zero Exponent Rule

States that $a^0 = 1$ for any nonzero number $a$.

Rational Expression

A fraction where the numerator and/or denominator are polynomials.

Difference of Squares

An expression of the form $a^2 - b^2$ that factors to $(a-b)(a+b)$.

Quadratic Equation

An equation of the form $ax^2 + bx + c = 0$ where $a \ne 0$.

Vertex Form of a Quadratic

A form of a quadratic function given by $f(x)=a(x-h)^2+k$.

X-Intercepts

The points where the graph crosses the x-axis, found by setting $f(x)=0$.

Y-Intercept

The point where the graph crosses the y-axis, found by evaluating $f(0)$.

Square Root Function

A function of the form $f(x)=\text{sqrt}(x)$ that is nonlinear.

Exponential Function

A function of the form $f(x)=a \times b^x$, representing constant multiplicative change.

Quadratic Function

A function represented as $f(x)=ax^2+bx+c$ that graphs as a parabola.

Domain

The set of all possible input values for a function.

Radicand

The expression inside a square root symbol.

Minimum Value

The lowest point on the graph of a function, particularly for parabolas that open upwards.

Maximum Value

The highest point on the graph of a function, particularly for parabolas that open downwards.

Ordered Pair

A pair of numbers that represent a point in a coordinate system, e.g., $(x,y)$.

Solving by Factoring

A method of solving equations by rewriting them as the product of factors.

Extraneous Solutions

Solutions that emerge from the solving process but do not satisfy the original equation.

Intersecting Lines

Solutions to a system of equations where graphs of equations cross at one point.

Completing the Square

A method used to solve quadratic equations by rewriting the expression in vertex form.

Intercepts

The points where a curve crosses the axes in a graph, relevant for understanding function behavior.

Symmetry

A property of parabolas indicating that one side is a mirror image of the other about the axis of symmetry.