GA Milestones Algebra EOC key terms

A letter or symbol that stands for a number whose value may change or is not yet known. Expressions and equations use variables to describe relationships in general form.

A fixed number in an expression or equation that does not change, such as the 5 in 3x + 5. It is separate from any variable term.

The number multiplied by a variable in a term, such as the 3 in 3x or the -2 in -2x². It tells how many of that variable part there are.

A single part of an expression separated by plus or minus signs, made of numbers, variables, or both multiplied together. For example, 4x² − 7y + 9 has three terms.

A mathematical phrase built from numbers, variables, and operations that has no equals sign, so it can be simplified or evaluated but not solved. Examples include 2x + 7 and (a − b)².

A statement that two expressions have equal value, joined by an equals sign. Solving an equation means finding the value or values of the variable that make the statement true.

A statement comparing two expressions with symbols such as <, >, ≤, or ≥ instead of an equals sign. Its solution is a range of values, often shown on a number line.

Terms that have exactly the same variable factors with the same exponents, such as 5x² and −3x². Only like terms can be combined by adding or subtracting their coefficients.

To rewrite an expression in an equivalent but more compact form by combining like terms, applying the distributive property, or reducing fractions, without changing its value.

The rule that a(b + c) = ab + ac, letting you multiply a factor across each term inside parentheses. It is also used in reverse to factor expressions.

The agreed sequence for evaluating expressions: grouping symbols first, then exponents, then multiplication and division left to right, then addition and subtraction left to right.

To find the numerical value of an expression by substituting given numbers for the variables and following the order of operations.

To replace a variable in an expression or equation with a specific number or another expression. Substitution is used both to evaluate expressions and to solve systems.

The measure of a line's steepness, equal to the change in y divided by the change in x between any two points. It describes the constant rate of change of a linear relationship.

The point where a graph crosses the y-axis, written as (0, b). In y = mx + b it is the value of y when x equals zero, often the starting amount in a model.

The equation y = mx + b, where m is the slope and b is the y-intercept. It makes graphing a line and writing an equation from a graph or table straightforward.

For a linear equation, the form Ax + By = C with integer coefficients and A ≥ 0. For a quadratic, the form ax² + bx + c, useful for identifying the y-intercept.

A function whose graph is a straight line and whose equation can be written as y = mx + b. It has a constant rate of change over equal intervals.

How much one quantity changes compared with another, calculated as change in output divided by change in input. For a linear function it equals the slope everywhere.

A rule that assigns exactly one output to each input in its domain. Passing the vertical line test confirms that a graph represents a function.

The set of all input values for which a function is defined. For example, the domain of f(x) = 1/x excludes x = 0 because division by zero is undefined.

The set of all output values a function actually produces. On a graph it is the collection of y-values covered by the curve or line.

Two or more equations considered together, whose solution is the set of values satisfying all of them at once. Graphically, it is where the lines or curves intersect.

A method for solving systems in which you add or subtract multiples of the equations to cancel one variable, then solve for the remaining variable.

Any value or set of values that makes an equation or inequality true. For a system, it must satisfy every equation in the system simultaneously.

The collection of all values that make an equation or inequality true. For inequalities it is usually an interval graphed on a number line.

A small raised number showing how many times the base is used as a factor, as in 2³ = 2 · 2 · 2. Exponent rules govern multiplication and division of powers.

An expression of the form bⁿ, where b is the base and n is the exponent. It represents repeated multiplication of the base.

In an exponential expression such as bⁿ, the number or variable being multiplied repeatedly. In exponential growth models it is the constant factor per interval.

An expression made of terms with nonnegative integer exponents, combined by addition or subtraction, such as 3x² − 5x + 1. Its degree is the largest exponent.

The greatest exponent on the variable in a polynomial or term. It determines the polynomial's end behavior and the maximum number of real roots.

To rewrite an expression as a product of simpler expressions, or one of those multiplied pieces. Factoring x² + 5x + 6 gives (x + 2)(x + 3).

A function of the form f(x) = ax² + bx + c with a ≠ 0, whose graph is a parabola. Its key features include the vertex, axis of symmetry, and intercepts.

The U-shaped graph of a quadratic function. It opens upward when a is positive and downward when a is negative, with a highest or lowest point called the vertex.

The highest or lowest point of a parabola, located on its axis of symmetry. It represents the maximum or minimum value of a quadratic function.

The vertical line through a parabola's vertex that divides it into mirror-image halves, given by x = −b/(2a) for f(x) = ax² + bx + c.

The rule that if a product equals zero, then at least one factor must equal zero. It is the key step in solving quadratic equations by factoring.

The values of x that make a polynomial equal zero; also called zeros or x-intercepts. A quadratic can have two, one, or no real roots depending on its discriminant.

The formula x = (−b ± √(b² − 4ac)) / (2a), which gives the solutions of any quadratic equation ax² + bx + c = 0, even when factoring fails.

The expression b² − 4ac from the quadratic formula. Its sign tells how many real solutions a quadratic has: positive gives two, zero gives one, negative gives none.

A function of the form f(x) = a · bˣ with b > 0 and b ≠ 1, where the variable is in the exponent. It models growth when b > 1 and decay when 0 < b < 1.

The base b in an exponential model, showing the multiplier applied each period. A growth rate of 8% corresponds to a growth factor of 1.08; a decay of 8% gives 0.92.

A sequence in which each term after the first is found by adding a constant difference. Its nth term is aₙ = a₁ + (n − 1)d.

The constant amount added from one term to the next in an arithmetic sequence. It equals the slope of the related linear function.

A sequence in which each term after the first is found by multiplying by a constant ratio. Its nth term is aₙ = a₁ · r^(n−1).

The constant multiplier between consecutive terms of a geometric sequence. It plays the same role as the growth factor in an exponential function.

The distance of a number from zero on the number line, always nonnegative. For example, |−7| = 7, and |x| = 3 has solutions x = 3 and x = −3.

A line on which numbers are placed by distance and direction from zero. It is used to graph inequalities, intervals, and absolute value relationships.

A graph plotting paired data points on a coordinate plane to show the relationship between two variables. Patterns suggest whether a linear or other model fits.

A line drawn through a scatter plot that comes closest to the data points and summarizes their trend. It can be used to predict values within or beyond the data range.

A statistical method that finds the line of best fit for data by minimizing squared distances from points to the line. The result is an equation used for prediction.

A measure of how strongly two variables are related in direction and strength, often described by a correlation coefficient between −1 and 1. Correlation does not prove causation.

A transformation that slides a graph without rotating or resizing it. Adding a constant to a function shifts its graph up or down; adding inside the input shifts it left or right.

A change to a parent graph's position, size, or orientation, including translations, reflections, stretches, and compressions. These changes correspond to altering parameters in the equation.

A transformation that flips a graph across a line, such as the x-axis or y-axis. Multiplying a function by −1 reflects it across the x-axis.

The simplest form of a family of functions, such as y = x, y = x², or y = |x|, from which related graphs are built through transformations.

A function that reverses another function's operations, so f and f⁻¹ undo each other. Its graph is the reflection of the original graph across the line y = x.

A rule that defines each term of a sequence using one or more previous terms, together with a starting value. For example, a₁ = 3 and aₙ = aₙ₋₁ + 4.

A rule that gives the nth term of a sequence directly in terms of n, so any term can be found without listing earlier ones. It is useful for modeling patterns.