Algebra Formulas Flashcards

Study Notes

Slope and Line Equations

Slope Formula: Used to determine the steepness of a line; denoted as m = (y₂ - y₁) / (x₂ - x₁).
Slope-Intercept Form: Represents linear equations in the form y = mx + b, where m is the slope and b is the y-intercept.
Point-Slope Form: A specific form for linear equations, expressed as y - y₁ = m(x - x₁), utilizes a known point (x₁, y₁) on the line.

Standard and Quadratic Forms

Standard Form: Represents linear equations in the format Ax + By = C, where A, B, and C are constants, often used for graphing.
Quadratic Formula: Used to find the roots of quadratic equations, given by x = (-b ± √(b² - 4ac)) / (2a).

Distance and Midpoint

Distance Formula: Calculates the distance between two points (x₁, y₁) and (x₂, y₂) as d = √((x₂ - x₁)² + (y₂ - y₁)²).
Midpoint Formula: Determines the exact midpoint between two points, calculated as M = ((x₁ + x₂)/2, (y₁ + y₂)/2).

Physics in Motion

Vertical Motion Model: Models the height of an object in free fall as h = -16t² + vt + s, where h is height, t is time, v is initial velocity, and s is initial height.

Geometry and Theorems

Pythagorean Theorem: Fundamental relation in Euclidean geometry for right triangles, expressed as a² + b² = c², relating the lengths of the sides.
X-Coordinate of Vertex of Quadratic: Determined using the formula x = -b/(2a), useful for finding the maximum or minimum point of a parabolic graph.

Description

Test your knowledge of essential algebra formulas with these flashcards. Each card features a key formula, such as the Slope Formula and Quadratic Formula, along with its definition. Perfect for students looking to reinforce their understanding of algebra concepts.