Algebra 2 Semester 1 Exam Formulas

Quadratic Functions

• Standard Form: A quadratic equation is expressed as f(x) = ax² + bx + c, where a, b, and c are constants.
• Vertex Calculation: The x-coordinate of the vertex for a parabola can be found using the formula x = -b/(2a).

Quadratic Function Forms

• Vertex Form: A quadratic function can also be written in vertex form as f(x) = a(x-h)² + k, where (h, k) represents the vertex.
• Quadratic Formula: Roots of a quadratic equation can be calculated using the formula x = [-b ± √(b²-4ac)]/(2a).

Polynomial Factorization

• Sum of Cubes: The expression a³ + b³ can be factored to (a + b)(a² - ab + b²).
• Difference of Cubes: The expression a³ - b³ factors to (a - b)(a² + ab + b²).
• Difference of Squares: The expression a² - b² factors to (a + b)(a - b).

Linear Equations

• Slope Definition: The slope of a line is calculated using the formula (y₂ - y₁)/(x₂ - x₁), representing the change in y over the change in x.
• Slope-Intercept Form: A linear equation can be represented as y = mx + b, where m is the slope and b is the y-intercept.
• Point-Slope Form: A linear equation can be expressed as y - y₁ = m(x - x₁), allowing for point-based graphing with a given point (x₁, y₁).