Algebra 2 Formulas Flashcards

Study Notes

Algebra 2 Key Formulas and Concepts

Quadratic Formula: Used to find the roots of a quadratic equation. The formula is (-b \pm \sqrt{b^2 - 4ac} / 2a).
Complex Number Standard Form: Represents a complex number as (a + bi), where (a) is the real part and (b) is the imaginary part.
Distance Formula: Calculates the distance between two points ((x_1, y_1)) and ((x_2, y_2)) using (\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}).
Midpoint Formula: Determines the midpoint coordinates between two points as (\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)).
Standard Form of a Line: Expresses a linear equation in the form (ax + by = c), where (a), (b), and (c) are constants.
Standard Form of a Circle: Represents a circle's equation as ((x - h)^2 + (y - k)^2 = r^2), where ((h, k)) is the circle's center and (r) is the radius.
Equation of a Line: Describes a line using the slope-intercept form (y = mx + b), where (m) is the slope and (b) is the y-intercept.
Point Slope Formula: Used to find the equation of a line when a point ((x_1, y_1)) and slope (m) are known, represented as (y - y_1 = m(x - x_1)).
Imaginary Numbers: Defined with (i) representing the imaginary unit, where (i^2 = -1), (i^3 = -i), and (i^4 = 1).
Set Notation: A way to represent a set mathematically, typically shown as ({x | \text{condition}}).
Interval Notation: A method of representing intervals on the number line, using parentheses for open intervals and brackets for closed intervals, e.g., ((x, y) \cup (a, b)).
Symmetry Tests:
- Even Function: Shows y-axis symmetry if replacing (x) with (-x) yields the original function.
- Odd Function: Displays origin symmetry if replacing (x) and (y) with (-x) and (-y) retrieves the original function.
Parallel and Perpendicular Lines:
- Parallel lines have equal slopes.
- Perpendicular lines' slopes are negative reciprocals of each other. Example: For line (y = -2x + 5), a parallel line will have a slope of (-2) and a perpendicular line will have a slope of (\frac{1}{2}).
Joint Variation: Describes a relationship where a variable varies directly in proportion to the product of other variables, represented as (k \times X).
Inverse Variation: Indicates a relationship where a variable varies inversely with another, shown as (k/X).
Function Determination: Defines a function as having only one output (y) for every input (x) in its domain.
Rate of Change: A measure of how a quantity changes over time, calculated as (\frac{f(x_2) - f(x_1)}{x_2 - x_1}).
Parabola Vertex Form: Expresses a parabola's equation as (y = a(x - h)^2 + k), where ((h, k)) is the vertex, and (a) indicates the direction of the parabola's opening (upward if (a > 0), downward if (a < 0)).

Description

Test your knowledge of essential Algebra 2 formulas with these flashcards. This quiz covers key topics such as the Quadratic Formula, Distance Formula, and Complex Numbers. Perfect for quick revision or in-depth study!