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?
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What is the sum of cubes formula?
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What is the difference of cubes formula?
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What is the difference of squares formula?
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What is the formula for slope in a linear equation?
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What is the slope-intercept form of a linear equation?
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What is the point-slope form of a linear equation?
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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).
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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.