MODULE 2

• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Writer: Randolf Byron S. Viray
• Cover Illustrator: Joel J. Estudillo
• MATHEMATICS Quarter 1: Module 2 Solving Quadratic Equations
• Department of Education National Capital Region SCHOOLS DIVISION OFFICE MARIKINA CITY
• Solve quadratic equations by

  Extracting square roots<|>Factoring<|>Completing the square<|>Quadratic formula
• You can say you have understood the lesson if you can

  • Extract square roots
  • Factor
  • Complete the square
  • Use Quadratic Formula
• Solving quadratic equations using extracting the square roots

  1. Solve for x2

  2. Extract the square roots of both sides

  3. If c ≥ 0, then √c represents the positive square root and -√c is the negative square root
• Solving quadratic equations by extracting the square roots

  • x2 = 81
  • 3x2 - 75 = 0
  • (w + 3)2 = 20
• In the equation ax2 + bx + c = 0, if b is equal to

  Zero, the new equation is ax2 = c
• Steps in solving quadratic equations by extracting the square root

  1. Solve for x2

  2. Extract the square roots of both sides

  3. If c ≥ 0, then √c represents the positive square root and -√c is the negative square root
• Solving quadratic equations using the Square Root Property

  1. 9x2 - 16 = 0

  2. (5x - 1)2 = 4/25
• Solving quadratic equations by extracting the square roots
• Solving quadratic equations by factoring
• Polynomial expressions to factor

  • 2m2 - 8m
  • -3x2 + 9x
  • 4x2 + 4
  • 10t2 + 2t
  • x2 + 4x + 4
  • y2 + 5y + 6
  • 8t2 + 4t
  • m2 + 6m + 9
  • 5t - 10t2
  • 10. 5x2 + 28x + 32
• Matching factors in Column A to polynomial expressions in Column B
• Solving quadratic equations by factoring

  1. Write the equation in ax2 + bx + c = 0 form<|>2. Factor the left member of the equation<|>3. Equate each factor to zero using zero product property<|>4. Solve the resulting first-degree equations<|>5. Check if the answers are correct by substituting them to the variable in the original equation
• Quadratic equations to solve using factoring

  • x2 + 5x + 6 = 0
  • x2 + 22x + 121 = 0
  • y2 - 25 = 0
  • 5a2 + 20a + 20 = 0
  • 4x2 + 20x + 25 = 0
• Completing the paragraph with appropriate terms
• Quadratic equation


  Equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0
• Solving quadratic equation by completing the square

  1. Divide both sides by a if a ≠ 1

  2. Group terms with variables on one side and constant term on the other side

  3. Add the square of half the coefficient of x to both sides

  4. Rewrite the resulting perfect square trinomial as the square of a binomial

  5. Extract the square root to solve for x
• Quadratic equations solved by completing the square

  • x^2 + 2x - 3 = 0
  • 2x^2 - 5x + 1 = 0
  • x^2 + 6x - 7 = 0
  • x^2 + 4x + 1 = 0
• 3x + 6 = 0 is not equal to 3(x + 2)^2 = 0
• Solving 3x + 6 = 0 by completing the square


  1. Divide both sides by 3

  2. x + 2 = 0

  3. x = -2
• The solution set for 3x + 6 = 0 is {-2}
• Beginning


  1
• Developing


  2
• Accomplished


  3
• Exemplary


  4
• Score


  • Neatness
  • Accuracy
  • Creativity
  • Time Management
• Neatness


  The scrap book was poorly created and difficult to read<|>The scrap book was sloppy and difficult to read<|>The scrap book is generally neat and readable<|>The scrap book was done very neat and easy to read
• Accuracy


  Majority of the data are incorrect and somehow irrelevant<|>The data are inaccurately represented contain major errors, or are missing<|>Data representation contains minor errors<|>All data are accurately represented
• Creativity


  A little creativity and some planning<|>Some creativity. Not enough planning<|>Good Creativity and mostly thought out<|>Well thought out and very creative
• Time Management

  The scrap book was submitted late 3-5 days after the deadline<|>The scrap book was submitted late 1-2 days after the deadline<|>The scrap book was submitted on time<|>The scrap book was submitted ahead of time
• Write down your personal insights and observations in doing this performance task
• Describe your personal realizations on how this task helps you see the real-world application of the topic: Solving Quadratic Equation by Completing the Square
• Initial step if the first term has a coefficient greater than one

  Divide both sides by this coefficient
• Third term in the quadratic equation x² - 20x + _____ to make it a perfect square trinomial

  100
• Solving quadratic equations by completing the square


  1. Write the equation in standard form

  2. Identify the values of a, b and c

  3. Subtract c from both sides

  4. Divide both sides by a

  5. Add (b/2a)^2 to both sides

  6. Factor the left side

  7. Extract the square root
• Solve the given quadratic equations by completing the square