MCAP Algebra 1 Flashcards

Quadratic Functions and Their Properties

• The vertex of a quadratic function can be found using the formula: x = -b/2a.
• The domain of any quadratic function is always (-∞, ∞), meaning it includes all real numbers.
• The standard form of a quadratic function is represented as f(x) = ax² + bx + c.
• A vertex is defined as the intersection of the parabola with its axis of symmetry, indicating the maximum or minimum point on the graph.

Functions and Their Characteristics

• A rational number can be expressed as the quotient of two integers, such as a/b where b ≠ 0.
• A function is defined as a relationship where each input is associated with one output.
• In a linear function represented as mx + b, the b value signifies the Y-intercept, or initial value of the function.

Slope and Its Interpretation

• The slope of a function indicates how much the output (y value) changes for a unit change in the input (x value), represented by the coefficient m in mx + b.
• For the linear function y = 2x + 3, the slope is exactly 2.

Graphical Analysis

• If x > 3, the shaded portion of the graph corresponds to the region from 3 to infinity, illustrating where the inequality holds true.
• The zero(s) of a function are the x-values where the output (y) equals zero.