Key Formulas in Precalculus

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(x₁ + x₂/2, y₁ + y₂/2)

√(x₂-x₁)²+(y₂-y₁)²

(f(x₂) - f(x₁)) / (x₂ - x₁)

<p>x = -b ± √(b² - 4ac) / 2a</p> Signup and view all the answers

<p>y - y₁ = m(x - x₁)</p> Signup and view all the answers

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Midpoint Formula
- Used to find the midpoint between two points (x₁, y₁) and (x₂, y₂) in a Cartesian plane.
- Formula: (x₁ + x₂)/2, (y₁ + y₂)/2
Distance Formula
- Computes the distance between two points (x₁, y₁) and (x₂, y₂).
- Formula: √((x₂ - x₁)² + (y₂ - y₁)²)
Rate of Change
- Measures how a quantity changes over an interval, important in calculus for derivatives.
- Formula: (f(x₂) - f(x₁)) / (x₂ - x₁)
Quadratic Equation
- A fundamental equation in algebra, used to find the roots of a quadratic function ax² + bx + c = 0.
- Formula: x = (-b ± √(b² - 4ac)) / (2a)
Point-Slope Form
- Equation of a line given a point (x₁, y₁) on the line and the slope m.
- Formula: y - y₁ = m(x - x₁)

These formulas are essential for various applications in geometry, algebra, and calculus, providing foundational skills for problem-solving and analysis in mathematics.