Algebra 2 Semester 1 Exam Formulas

Questions and Answers

What is the standard form of a quadratic equation?

f(x) = ax^2 + bx + c

What is the formula to find the vertex of a quadratic equation?

x = -b/2a

What is the vertex form of a quadratic function?

f(x) = a(x-h)^2 + k

What is the quadratic formula?

-b±[√b²-4ac]/2a Signup and view all the answers

What is the sum of cubes formula?

a^3 + b^3 = (a + b)(a^2 - ab + b^2) Signup and view all the answers

What is the difference of cubes formula?

a^3 - b^3 = (a - b)(a^2 + ab + b^2) Signup and view all the answers

What is the difference of squares formula?

a^2 - b^2 = (a + b)(a - b) Signup and view all the answers

What is the formula for slope in a linear equation?

(y₂ - y₁) / (x₂ - x₁) Signup and view all the answers

What is the slope-intercept form of a linear equation?

y = mx + b Signup and view all the answers

What is the point-slope form of a linear equation?

y - y1 = m(x - x1) Signup and view all the answers

Study Notes

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).

Description

This quiz features flashcards covering essential formulas for Algebra 2, Semester 1. You'll learn about quadratic equations, vertex forms, the quadratic formula, and more. Use these flashcards to prepare effectively for your exam.