Algebra 2 Flashcards

Study Notes

Slope-intercept Form: Expressed as y = mx + b, where m is the slope and b is the y-intercept.
Standard Form: Written as Ax + By = C, encompassing all linear equations.
Point-Slope Form: Given as y - y1 = m(x - x1) for a line passing through point (x1, y1) with slope m.
Real Numbers: Consist of both rational and irrational numbers, encompassing all possible values along the number line.
Order of Operations (PEMDAS): A mnemonic for solving expressions in the order of Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

No Solution: Occurs when contradictory equations, e.g., 10 = -3, arise when solving.
All Real Numbers: Happens when the equation simplifies to a true statement, such as 0 = 0.
Relation: A pairing of input and output values, typically represented as coordinate points (x, y).
Domain: The set of all possible input values (x values) for a relation.
Range: The collection of all output values (y values) corresponding to the domain.

Function: A relation where each input has exactly one output; x values cannot repeat.
Vertical Line Test: A graphical method to determine if a relation is a function; a vertical line should intersect the graph at most once.
Function Notation: Represented as f(x), indicating the value of the function for a given x.

Slope (m): Defined as rise/run, or (y2 - y1) / (x2 - x1).
Positive Slope: Indicates an upward line.
Negative Slope: Represents a downward line.
Zero Slope: Characterizes a horizontal line.
Undefined Slope: Pertains to a vertical line, denoted as m = number/0.
Parallel Lines: Lines with identical slopes that never intersect.
Perpendicular Lines: Lines intersecting at right angles; their slopes are opposite reciprocals, e.g., m1 * m2 = -1.

Quadratic Formula: x = -b ± √(b² - 4ac) / 2a, used to find roots of quadratic equations.
Discriminant (b² - 4ac): Indicates the nature of the roots of a quadratic equation;
- Greater than zero indicates two real solutions.
- Equal to zero indicates one real solution.
- Less than zero indicates two imaginary solutions.
Completing the Square: A method for solving quadratic equations, rearranging them into a perfect square trinomial.

Vertex: The highest or lowest point of a parabola formed by a quadratic function.
Axis of Symmetry: The vertical line that divides the parabola into two symmetrical halves, passing through the vertex.
Graphing Quadratic Inequalities:
- Parabola drawn based on the inequality type; dashed for > or <, solid for ≥ or ≤.
- Test points inside the parabola to determine shaded regions.

Rational Zero Theorem: Provides potential rational roots based on the factors of the constant term and leading coefficient.
Factor Theorem: States that (x - k) is a factor of polynomial f(x) if f(k) = 0.
Remainder Theorem: The remainder of f(x) divided by (x - k) is f(k).
Fundamental Theorem of Algebra: Asserts that any polynomial of degree n has at least one complex root.

Complex Conjugates: Two complex numbers of form a + bi and a - bi; their product yields a real number.
Absolute Value of Complex Numbers: Calculated as |z| = √(a² + b²), where a and b are real and imaginary components respectively.