Algebra 1 STAAR Review Flashcards

Key Concepts in Algebra 1

• Rate of Change: Equivalent to the slope of a line, indicating how much one variable changes in response to another.
• Independent Variable: Represented by "X"; the value that can be controlled or changed in an equation.
• Dependent Variable: Represented by "Y"; its value depends on the independent variable.
• Solution, Zero, Root: All terms referring to the X-Intercept, where the graph crosses the X-axis (Y=0).

Types of Numbers

• Rational Numbers: Can be expressed as a/b (a and b are integers, b ≠ 0); includes integers, fractions, and decimals that terminate or repeat.
• Irrational Numbers: Cannot be expressed as fractions; includes non-repeating, non-terminating decimals and square roots of non-perfect squares.
• Perfect Squares: Result from squaring an integer; their square roots are always whole numbers.

Algebraic Variables and Functions

• Variables: Symbols representing numbers in equations or expressions.
• Direct Variation: Relationship where an increase in X results in an increase in Y; they vary directly.
• Inverse Variation: Relationship where an increase in X results in a decrease in Y; they vary inversely.

Coordinate Plane Features

• Origin: The point (0,0) where the X and Y axes intersect.
• Quadrants: The four sections of a coordinate plane formed by the X and Y axes.
• X-Axis and Y-Axis: The horizontal and vertical lines on a graph, respectively.

Graphical Transformations

• Translation: A transformation that shifts a graph horizontally and/or vertically without altering its shape.
• Reflection: A transformation that flips a figure over a line, creating a mirror image.

Function Characteristics

• Vertical Line Test: A method to determine if a graph represents a function; a function passes if every vertical line intersects the graph at one point.
• Relation: A set of ordered pairs, representing the relationship between X and Y.
• Domain: The set of all first coordinates (X-values) in a relation.
• Range: The set of all second coordinates (Y-values) in a relation.

Types of Functions

• Linear Function: A function whose graph forms a straight line.
• Slope: Defines the steepness of a line calculated as the change in Y over the change in X.
• Dilation: A transformation resulting in the enlargement or reduction of a figure.

Polynomial Terms

• Monomial: A single term polynomial.
• Polynomials: The sum or difference of multiple monomials.
• Binomial: The sum or difference of two monomials.
• Trinomial: The sum or difference of three monomials.

Specific Functions

• Parabola: The graph shape of a quadratic function.
• Vertex: The highest or lowest point on a parabola.
• Axis of Symmetry: The line that divides a parabola into two mirror-image halves.

Midpoint and Line Concepts

• Midpoint: The point located equidistantly between the endpoints of a segment.
• Slope of a Line: Represents the rate of change between two points on a line.
• Quadratic Formula: A method for solving quadratic equations.
• Slope-Intercept Form: The equation of a line expressed as y = mx + b, where m is the slope and b is the y-intercept.
• Point-Slope Form: Another way to represent the equation of a line, typically used for finding slopes through a given point.