Algebra Vocabulary Flashcards

Algebra Vocabulary Study Notes

• Variable: Represents an unknown number, commonly denoted by letters (e.g., x, y).

• Equation: A statement asserting the equality of two expressions, often containing variables.

• Distributive Property: Establishes that for all real numbers a, b, and c, the equation a(b + c) = ab + ac holds true.

• Formula: An equation that reveals how different measurements relate to each other, often used in various fields of study.

• Coefficient: A numerical factor that multiplies a variable in an expression, affecting its value.

• Opposite: The negative counterpart of a real number a, represented as -a.

• Reciprocal: For a nonzero real number a, its reciprocal is defined as 1/a, crucial in division operations.

• Factor: The process of expressing a number or expression as a product of its components.

• Power: Refers to an expression where a number, called the base, is multiplied by itself a specified number of times.

• Polynomial: A mathematical expression that is the sum of one or more monomials.

• Binomial: A specific type of polynomial that contains exactly two terms.

• Prime Polynomial: A polynomial that cannot be factored further, having a greatest monomial factor of 1.

• Integers: Include all whole numbers and their negative counterparts, forming a complete set of opposites.

• Quadratic: A polynomial of degree two, characterized by its highest exponent, providing a rich field for solutions.

• Ordered Pair: Two elements represented in a specific order, e.g., (x, y), essential for graphing coordinates.

• Coordinate System: A framework comprising two intersecting number lines (axes) used for graphing ordered pairs.

• Solution: An ordered pair that makes an equation true, representing a point of intersection in graphing.

• Graph: A visual representation of all points that satisfy a particular equation, illustrating relationships between variables.

• Slope: Reflects the steepness of a line, calculated as the ratio of the difference in y-coordinates to the difference in x-coordinates, also termed rise over run.

• Y-Intercept: The specific point where a graph crosses the y-axis, defined by its y-coordinate when x=0.

• Slope-Intercept Form: The standard form of a linear equation written as y = mx + b, where m signifies slope and b signifies the y-intercept.

• System of Equations: A collection of two or more equations that share common variables, often solved simultaneously.

• Function: A relation characterized by unique first elements (inputs) for each ordered pair, ensuring no repetition.

• Direct Variation: A relationship defined by y = kx, where k is a nonzero constant, signifying proportionality between x and y.

• Inverse Variation: Represented by y = k/x, where k is a nonzero constant, indicating an inverse relationship between x and y.

• Radical: An expression involving roots, typically seen in square root forms, essential in simplifying equations.

• Quadratic Formula: A solution method for quadratic equations, given by x = -b±√(b²-4ac)/(2a), applicable when a is not zero.

• Parabola: The graphical representation of a quadratic function, displaying a distinct U-shape on the coordinate plane.