Algebra Class: Equations
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Questions and Answers

What is the general form of a linear equation?

  • ax + by = c (correct)
  • ax^2 + bx + c = 0
  • x + by = c
  • x^2 + bx + c = 0

    • What is the formula to solve quadratic equations when factoring is not possible?

  • x = (b ± √(b^2 - 4ac)) / a
  • x = (-b ± √(b^2 - 4ac)) / 2a (correct)
  • x = (b ± √(b^2 + 4ac)) / 2a
  • x = (-b ± √(b^2 + 4ac)) / 2a

    • What is the method to solve a system of equations where you solve one equation for one variable and substitute it into another equation?

  • Elimination
  • Substitution (correct)
  • Graphing
  • Factoring

    • What is the key feature of a quadratic equation graph that is the point where the axis of symmetry intersects the graph?

    <p>Vertex</p> Signup and view all the answers

    What is the definition of a quadratic equation?

    <p>An equation with a highest power of 2 for the variable.</p> Signup and view all the answers

    What is the method to express a quadratic equation as a product of two binomials?

    <p>Factoring</p> Signup and view all the answers

    Study Notes

    Algebraic Equations

    • Linear Equations:
      • Definition: An equation in which the highest power of the variable (usually x) is 1.
      • General form: ax + by = c, where a, b, and c are constants.
      • Example: 2x + 3 = 7
    • Quadratic Equations (covered in more detail below)
    • Systems of Equations:
      • Definition: A set of two or more equations with two or more variables.
      • Methods to solve:
        • Substitution
        • Elimination
      • Example: 2x + 3y = 7, x - 2y = -3

    Quadratic Equations

    • Definition: An equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.
    • Factoring:
      • Definition: Expressing a quadratic equation as a product of two binomials.
      • Example: x^2 + 5x + 6 = (x + 3)(x + 2) = 0
    • Quadratic Formula:
      • Definition: A formula to solve quadratic equations when factoring is not possible.
      • Formula: x = (-b ± √(b^2 - 4ac)) / 2a
      • Example: Solve x^2 + 4x + 4 = 0
    • Graphing Quadratic Equations:
      • Definition: A visual representation of a quadratic equation on a coordinate plane.
      • Key features:
        • Vertex (h, k)
        • Axis of symmetry
        • x-intercepts

    Algebraic Equations

    • Linear Equations:
      • Defined as equations with the highest power of the variable (usually x) being 1
      • General form: ax + by = c, where a, b, and c are constants
      • Example: 2x + 3 = 7

    Quadratic Equations

    • Definition: Equations of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0
    • Factoring:
      • Expressing a quadratic equation as a product of two binomials
      • Example: x^2 + 5x + 6 = (x + 3)(x + 2) = 0
    • Quadratic Formula:
      • Formula to solve quadratic equations when factoring is not possible
      • Formula: x = (-b ± √(b^2 - 4ac)) / 2a
      • Example: Solve x^2 + 4x + 4 = 0
    • Graphing Quadratic Equations:
      • Visual representation of a quadratic equation on a coordinate plane
      • Key features:
        • Vertex (h, k)
        • Axis of symmetry
        • x-intercepts

    Systems of Equations

    • Definition: A set of two or more equations with two or more variables
    • Methods to solve:
      • Substitution
      • Elimination
    • Example: 2x + 3y = 7, x - 2y = -3

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    Description

    Learn about linear equations, quadratic equations, and systems of equations in algebra. Understand definitions, general forms, and examples of each type of equation.

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