MODULE 11

• Discipline

  Good Taste
• Writer: Gemma Y. Bandoquillo
• Cover Illustrator: Joel J. Estudillo
• Department of Education, National Capital Region, SCHOOLS DIVISION OFFICE, MARIKINA CITY
• Quadratic function


  Function in the form y = (x - h)^2 + k
• Analyze the effects of changing the values of a, h and k in the equation y = (x - h)^2 + k of a quadratic function on its graph


  1. Graph vertical and horizontal shifts of quadratic functions

  2. Graph vertical compressions and stretches of quadratic functions

  3. Describe the movement of the graph of quadratic function
• Increasing the value of a

  Graph gets narrower
• Decreasing the value of a

  Graph gets narrower
• h > 0

  Graph slides h units to the right
• h < 0


  Graph slides h units to the left
• Increasing the value of k

  Graph shifts vertically upward
• Decreasing the value of k

  Graph shifts vertically downward
• Quadratic function


  A function of the form y = ax^2 + bx + c, where a, b, and c are constants
• Effects of the value k on the graph of quadratic function

  1. If k > 0, the graph of the quadratic function slides k units upward

  2. If k < 0, the graph of the quadratic function slides k units downward
• Effects of the value h on the graph of quadratic function

  1. If h > 0, the graph of the function slides h units to the right

  2. If h < 0, the graph of the function slides h units to the left
• Graph of y = 2(x - 4)^2


  Same as the graph of y = 2x^2 but slides 4 units to the right
• If h > 0, the graph of the function slides h units to the right
• If h < 0, the graph of the function slides h units to the left
• If k > 0, the graph of the quadratic function slides k units upward
• If k < 0, the graph of the quadratic function slides k units downward
• Sketch the graph of each quadratic function

  1. f(x) = 2x^2 + 3

  2. f(x) = 2(x - 3)^2 - 1

  3. f(x) = 2(x + 2)^2

  4. f(x) = -2x^2 + 3

  5. f(x) = 2(x + 1)^2 - 2

  6. f(x) = 2(x + 4)^2

  7. f(x) = -2x^2 - 1

  8. f(x) = 2(x + 3)^2 + 5

  9. f(x) = 2(x - 3)^2 - 2

  10. 10. f(x) = -2(x - 1)^2
• Opening of the graph


  • Indicates whether the graph opens upward or downward
• Vertex


  • The point where the graph changes direction
• Movement of the graph


  • Indicates how the graph shifts horizontally or vertically
• y

  Dependent variable
• x


  Independent variable
• Transforming quadratic functions

  1. Shifting left/right

  2. Shifting up/down

  3. Stretching/compressing
• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Statements to be evaluated

  • I. The graph of y = -5x^2 is narrower than the graph of y = -3x^2.
  • II. The graph of the function y = (x + 2)^2 - 5 is obtained when the graph of y = x^2 slides 2 units to the left and 5 units downward.
• Bryant, Merden l.,Bulalayao , Leonides E.Callanta, Merlyn M.,Cruz Jerry D., De Vera Richard F., Garcia Gilda T.Javier SoniaE.Lzaro,Roselle A.Mesterio, Bernadette J.& Saladino, Rommel Hero A.(2014) Mathematics 9 Learner's Material.department of Education ,Republic of the Philippines, Vibal Group Publishing Inc.,Pasig City
• Coronel, Iluminada C F.M.M. , Villano, Ma.Luisa V., Manalastas Jr., Pablo R., Marasigan, Jose A.,Coronel , Antonio C. (!991) Mathemtics 3, Bookmark Inc. 264 Vito Cruz Extension , Makati City Metro Manila Phil.
• Mallari, Ma.Theresa G., Gabriel ,Judy, Villareal , Abelardo A. ,Argel , Analyn M.,Semira, Gemmalyn T., Angeles, Alma , Gestoso, Barnie, Amid , Diego M.,Tibulan,Mike T.(2019) Mathtime , Educational Resources Corporated 11-B Sunrise Drive Barangay bagong Lipunanng Crame Cubao Quezon City.