Algebra And Functions: Math Terms Explained
Plain-language definitions of every algebra and functions term your child meets in school, each with kid-friendly explanations, worked examples, and common mistakes to watch for.
Arithmetic sequence
An arithmetic sequence is a list of numbers where you add or subtract the same amount each time to get from one term to the next, so the difference between any two neighboring terms is always the same.
Binomial
A binomial is an algebraic expression that is the sum or difference of exactly two terms, such as 3x + 5 or x − 4, and it is often used in factoring, expanding powers, and modeling binomial probability situations.
Completing the square
Completing the square is a method for rewriting a quadratic expression or equation so that part of it becomes a perfect square, which makes it easier to solve or to see key features like the vertex of a parabola.
Direct variation
Direct variation is a relationship between two variables where one is always a constant multiple of the other, so their ratio stays the same and the graph is a straight line through the origin.
Discriminant
A discriminant is the expression under the square root in the quadratic formula, written as b² − 4ac, that tells you how many solutions a quadratic equation has and whether those solutions are real or not real.
Domain
A domain is the complete set of input values for which a relation or function is defined and produces valid outputs.
Domain and range
Domain and range are two parts of describing a function: the domain is all the input values that are allowed, and the range is all the output values the function can produce.
Equation
An equation is a math statement that shows two things are equal, using an equals sign, and it can be checked by seeing if the values on both sides are the same.
Exponential decay
Exponential decay is a type of exponential function where a quantity decreases by the same percentage in each equal time step, so it gets smaller and smaller but never reaches zero in a finite number of steps.
Exponential function
An exponential function is a function where the variable is in the exponent, typically written in the form f(x) = a · bx, and the output changes by the same factor (is multiplied) over equal steps in x instead of changing by the same amount.
Exponential growth
Exponential growth is a type of change where a quantity increases by the same percentage or factor in each equal time step, so its value speeds up and grows faster and faster over time.
Factoring
Factoring is rewriting a number or algebra expression as a product, which means as two or more factors multiplied together, in a way that does not change its value.
Function
A function is a rule that pairs each input value with exactly one output value, often written as y or f(x), and can be shown with tables, equations, graphs, or mapping diagrams.
Function notation
Function notation is a way of writing a function using a name like f and an input in parentheses, such as f(x), to show how each input is paired with exactly one output.
Geometric sequence
A geometric sequence is a list of numbers where each term is found by multiplying the previous term by the same constant number, called the common ratio, which creates a nonlinear, exponential pattern.
Inequality
An inequality is a math statement that compares two quantities using symbols like <, >, ≤, or ≥ to show that they are not necessarily equal.
Input and output
Input and output are pairs of numbers where a rule takes an input value, applies the same rule every time, and produces an output value.
Linear equation
A linear equation is an equation where each variable is only to the first power and whose graph forms a straight line, often written in forms like y = mx + b or ax + b = c.
Linear function
A linear function is a function whose graph is a straight line, which can be written in the form y = mx + b where m is the constant rate of change (slope) and b is the y-intercept.
Literal equation
A literal equation is an equation made up mostly of letters (variables) that can be solved or rearranged to isolate one chosen variable in terms of the others.
Logarithm
A logarithm is an operation that tells you what exponent you put on a base number to get a certain result, for example log2(8) = 3 because 23 = 8.
Monomial
A monomial is an algebraic expression that is a single term, made from a number, a variable, or a product of numbers and variables with whole-number exponents.
Negative slope
A negative slope is the rate of change of a line when its y-value decreases as the x-value increases, which appears as a line that slants downward from left to right on a coordinate graph.
One-step equation
A one-step equation is an equation that can be solved by performing just one operation, such as a single addition, subtraction, multiplication, or division, to find the value of the unknown.
Parabola
A parabola is a U-shaped curve that is the graph of a quadratic function and can also be defined as the set of all points that are the same distance from a fixed point called the focus and a fixed line called the directrix.
Perfect square trinomial
A perfect square trinomial is a polynomial with three terms that can be written as the square of a binomial, such as x2 + 6x + 9 = (x + 3)2.
Point-slope form
Point-slope form is a way to write the equation of a straight line using its slope and the coordinates of one point on the line, usually written as y − y₁ = m(x − x₁).
Polynomial
A polynomial is an algebraic expression made by adding and subtracting terms that each look like a number times a variable raised to a whole-number exponent, such as 5x3 or -2x.
Quadratic equation
A quadratic equation is an equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are numbers and a is not 0, and its solutions are the values of the variable that make the equation true.
Quadratic formula
The quadratic formula is a step-by-step rule that gives the solutions (also called roots) of any quadratic equation written in the form ax² + bx + c = 0, using the numbers a, b, and c from the equation.
Radical
A radical is a math symbol used to show a root, such as a square root or cube root, written with the root sign √ and possibly a small index number.
Rational expression
A rational expression is an expression that can be written as one polynomial divided by another polynomial, where the denominator polynomial is not zero.
Sequence
A sequence in math is an ordered list of numbers or objects that follow a specific rule or pattern, where each item in the list is called a term.
Slope
Slope is the number that describes how steep a straight line is, found by dividing the vertical change (rise) by the horizontal change (run) between any two points on the line.
Solving equations
Solving equations is the process of finding all values of a variable that make an equation true, using step-by-step operations that keep both sides of the equation equal.
System of equations
A system of equations is a set of two or more equations that are all true for the same values of the variables, and the solution is any value or values that make every equation in the set true at the same time.
Trinomial
A trinomial is a polynomial that has exactly 3 terms, usually written as a sum or difference of variable parts and numbers, such as x^2 + 5x - 6.
Two-step equation
A two-step equation is a one-variable equation that can be solved by using two inverse operations, such as undoing addition or subtraction and then undoing multiplication or division, to find the value that makes the equation true.
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