Key Algebra Terms Quiz

Key Algebra Terms

• Absolute Value Function: Defined as f(x)=|x|, this function always yields non-negative values, where f(x) ≥ 0 for all x.

• Axis of Symmetry: A vertical line through the vertex of a parabola, acting as a mirror that divides it into two symmetric halves.

• Completing the Square: A method used to convert a binomial of the form x² + bx into a perfect square trinomial by adding a constant term.

• Dilation: Refers to a transformation that scales the size of a figure while preserving its shape.

• Discriminant: In the quadratic formula, represented by the expression b² - 4ac, this determines the nature of the roots.

• Double Root: Occurs in a quadratic function when both roots are the same, indicating a repeated solution.

• Greatest Integer Function: Notated as f(x) = [|x|], it outputs the largest integer less than or equal to x, creating a step-like graph.

• Maximum: The highest point that can be reached on the graph of a curve, representing the maximum value of the function.

• Minimum: The lowest point on the graph of a curve, representing the minimum value of the function.

• Parabola: The graphical representation of a quadratic function, characterized by its U-shape.

• Piecewise Defined Function: A function composed of multiple expressions, each applicable to specific intervals of the input variable.

• Piecewise Linear Function: A type of piecewise function that consists of linear expressions across its defined intervals.

• Quadratic Formula: Used for solving quadratic equations of the form ax² + bx + c = 0, provided a ≠ 0. Expressed as x = (-b ± √(b² - 4ac)) / (2a).

• Quadratic Function: An equation defined as ax² + bx + c, where a ≠ 0, representing a parabolic relationship between variables.

• Reflection: A transformation that flips a figure across a line, especially relevant when a negative sign precedes the quadratic term in a function.

• Standard Form: The format ax + by = c for linear equations, adhering to constraints where a ≥ 0, both a and b are not zero, and the coefficients are integers with a greatest common factor of 1.

• Step Function: Exhibits a graph composed of horizontal line segments, creating steps in the function’s value.

• Transformation: Describes any movement made to a geometric figure, whether through translation, reflection, dilation, or rotation.

• Translation: A specific type of transformation where a figure shifts its position without rotation or resizing.

• Vertex: Represents the peak or lowest point of a parabola, where either maximum or minimum occurs, crucial for understanding the parabola's behavior.