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Key Formulas in Precalculus
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Key Formulas in Precalculus

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Questions and Answers

What is the formula for the midpoint?

(x₁ + x₂/2, y₁ + y₂/2)

What is the formula for distance between two points?

√(x₂-x₁)²+(y₂-y₁)²

What is the formula for rate of change?

(f(x₂) - f(x₁)) / (x₂ - x₁)

What is the quadratic equation?

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

What is the point slope formula?

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

Study Notes

Key Formulas in Precalculus

  • 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)

Summary of Importance

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

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Description

This quiz covers essential formulas used in precalculus, including the midpoint and distance formulas, rate of change, the quadratic equation, and point-slope form. Understanding these concepts is vital for success in higher-level mathematics such as calculus and algebra. Test your knowledge and strengthen your math skills with this quiz.

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