MODULE 1

• City of Good Character
• Characteristics of the City of Good Character

  • Discipline
  • Good Taste
  • Excellence
• Writer: Randolf Byron S. Viray
• Cover Illustrator: Joel J. Estudillo
• Department of Education, National Capital Region, SCHOOLS DIVISION OFFICE, MARIKINA CITY
• Hello Grade 9 learners! In this module, you will learn how to: Illustrate Quadratic Equation's M9AL-Ia-1
• You can say that you have understood the lesson in this module if you can already:

  • Determine equations whether it is quadratic or not quadratic
  • Determine the numerical coefficients of the standard form of quadratic equation
  • Illustrate quadratic equations
• Quadratic Equation


  A polynomial equation of degree two that can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0
• Standard Form of Quadratic Equation


  ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0
• Quadratic Equations in Standard Form

  • x^2 + 4x + 3 = 0
  • x^2 - 1 = 3
  • 1/3 x^2 - 7 = -2x
  • x^2 + 4x + 4 4/3 + x = 0
  • 2x^2 + 8x = 15
• Complete Quadratic Equation


  ax^2 + bx + c = 0
• Incomplete Quadratic Equation


  ax^2 + c = 0

  ax^2 + bx = 0

  ax^2 = 0
• Incomplete Quadratic Equations


  • 2x^2 + 9 = 0
  • x^2 - 9x = 0

  2x^2/3 = 0
• Edna: a = -2, b = 3, c = 5

  Jane: a = 2, b = -3, c = -5

  Luisa: a = 2, b = 3, c = -5

  Christy: a = -2, b = -3, c = -5
• Edna got the correct values of a, b, and c in the given equation 5 - 3x = 2x^2
• Quadratic Equations


  • x^2 + 1 = (x + 3)^2

  x(x + 2)

  x + 1/x = 2

  x + 1/x
• Quadratic Equation


  An equation whose degree exponent is equal to two
• A number is eight more than another number. If the product of the two numbers is twenty, what are the numbers?
• Solving the Word Problem

  Represent the two numbers as variables

  Set up an equation to represent the relationship between the numbers

  Solve the equation to find the two numbers
• Quadratic Equation in One Variable

  A mathematical sentence of degree 2 that can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0
• Quadratic Term


  ax^2
• Linear Term


  bx
• Constant Term


  c
• Quadratic Equations


  • 8x^2 + 14x - 17 = 0

  6x(x - 4) = 20

  (4x + 7)(2x - 2) = -16
• 1.5y - 6 = -y^2 is a quadratic equation in standard form with a = 1, b = 5, c = -6
• 5w - 12 is not a quadratic equation, it is a linear equation
• 5v^2 - 3v = -4 is a quadratic equation in standard form with a = 5, b = -3, c = 4
• x^2 + 7x = x^3 - 5 is not a quadratic equation, it is a polynomial equation of degree 3
• x^2 + 3x + 7 is not a quadratic equation, it is a polynomial expression
• Incomplete Quadratic Equation


  When b = 0 in the equation ax^2 + bx + c = 0, it results in a quadratic equation of the form ax^2 + c = 0
• Quadratic equation


  Equation of the form ax^2 + bx + c = 0
• Quadratic equations


  • Can be complete or incomplete
  • Complete if no coefficient is equal to 0
  • Incomplete if either coefficient b or c is equal to 0
  • When a = 1, it is a standard form equation
• Quadratic equations in standard form

  • 5x^2 + 3x - 2 = 0
  • 2x^2 - 4x + 1 = 0
  • x^2 + 5x + 6 = 0
  • 3x^2 - 2x - 1 = 0
  • x^2 - 7x + 10 = 0
• The linear term in a quadratic equation ax^2 + bx + c = 0 is bx
• The quadratic term in a quadratic equation ax^2 + bx + c = 0 is ax^2
• Incomplete quadratic equation


  Either the coefficient b or c is equal to 0
• Complete quadratic equation


  No coefficient is equal to 0
• A linear equation has 1 root, a quadratic equation has 2 possible roots