Unit 9 – Equations: Basics of Statistics and Mathematics

Vocabulary flashcards summarizing essential terms and definitions from Unit 9 (Equations) of BCOM304: Basics of Statistics & Mathematics.

Equation

A mathematical statement that sets two algebraic expressions equal using the “=” sign.

Variable

A symbol representing an unknown quantity whose value can change (e.g., x, y).

Constant

A fixed numerical value that does not change within an equation.

Coefficient

The numerical factor multiplied by a variable (e.g., 3 in 3x).

Degree (of an equation)

The highest power (sum of exponents) of the variable(s) in an equation.

Root of an Equation

A value of the variable that satisfies the equation, making both sides equal.

Left-Hand Side (LHS)

The expression written to the left of the equal sign in an equation.

Right-Hand Side (RHS)

The expression written to the right of the equal sign in an equation.

Transposition

The process of moving a term from one side of an equation to the other, changing its sign.

Linear Equation

An equation whose degree is 1; its graph is a straight line.

Quadratic Equation

An equation of the form ax² + bx + c = 0 with a≠0; its graph is a U-shaped curve.

Cubic Equation

An equation of degree 3 (highest power ³).

Polynomial (General)

An algebraic expression or equation of degree greater than 3.

Linear Equation (One Variable)

A degree-1 equation involving a single unknown (e.g., 3x + 8 = 14).

Linear Equation (Two Variables)

A degree-1 equation involving two unknowns (e.g., 2x + 7y = 26).

Discriminant (Δ)

For ax² + bx + c = 0, the value b² − 4ac that determines the nature of the roots.

Real and Distinct Roots

Roots that are real numbers and unequal; occurs when Δ > 0.

Real and Equal Roots

Identical real roots; occurs when Δ = 0.

Imaginary (Complex) Roots

Non-real roots; occur when Δ < 0.

Nature of Roots

Classification of roots (real distinct, real equal, or imaginary) based on the discriminant.

Factorization Method

Solving a quadratic by expressing it as (x − α)(x − β)=0 and setting each factor to zero.

Sum of Roots (Quadratic)

For ax² + bx + c = 0, α + β = −b⁄a.

Product of Roots (Quadratic)

For ax² + bx + c = 0, αβ = c⁄a.

Starting Point (Base Value)

The initial value from which change begins in a linear relationship.

Constant Rate of Change

A fixed amount by which one quantity increases or decreases relative to another (linear).

Turning Point

The highest or lowest point on the graph of a quadratic equation.

U-Shaped Curve

The parabolic graph of a quadratic equation; opens up or down.

Straight-Line Relationship

A direct, constant-rate connection between two quantities (linear).

Curved Relationship

A non-constant, accelerating or decelerating connection between quantities (quadratic).

Graph

A visual representation of an equation; linear graphs are lines, quadratic graphs are parabolas.

Curved Path

The trajectory described by quadratic relationships, such as a projectile’s motion.

Acceleration

Rate of change of velocity; creates non-constant changes modeled by quadratic equations.

Constant Change

A feature of linear equations where increments remain uniform.

Non-Constant Change

Variable rate of change characteristic of quadratic (and higher-degree) equations.

Transposition Rule

When a term crosses the equal sign, its sign reverses ( + ↔ − ).