MODULE 8

• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Writer: Roselyn R. Baracuso
• Cover Illustrator: Joel J. Estudillo
• MATHEMATICS Quarter 1: Module 8 Quadratic Functions
• Department of Education National Capital Region SCHOOLS DIVISION OFFICE MARIKINA CITY
• Model quadratic functions in real-life situations

  M9AL-If-10
• Represent quadratic functions using: (a) table of values

  M9AL-Ig-11.0
• Represent quadratic functions using: (b) graph

  M9AL-Ig-11.1
• Represent quadratic functions using: (c) equation

  M9AL-Ig-11.2
• Lessons in this module

  • Lesson 1: Models of Quadratic Functions
  • Lesson 2: Ways of Presenting Quadratic Functions
• After going through this module, you are expected to: 1. model real-life situation using quadratic functions; 2. represent quadratic function using table of values, graph and equation; and 3. appreciate the relevance of quadratic functions in real life situations.
• General form of a quadratic function

  f(x) = ax^2 + bx + c
• Degree of variable x in a quadratic function

  2
• Equations representing quadratic functions

  • f(x) = 4x^2 + 3
  • 3y^2 - 5 = x
  • y = 4x - 52
  • y = 3x - 7
• Given the function f(x) = -x^2 + 2x - 3, the values of a, b and c

  a = -1, b = 2, c = -3
• Situations modelling quadratic functions

  • Throwing a ball upward
  • Path of a launching airplane
• Given the quadratic function f(x) = x^2 + x - 1, the values of f(x) when x = -1, 0 and 1


  f(-1) = -1, f(0) = 0, f(1) = 1
• Correct table of values for the function f(x) = x^2 + 1

  • x = -3 to 3, y = -9 to 9
• Graph of a quadratic function

  Parabola
• To know if a table of values represents a quadratic function

  If the second differences in y are equal
• Graph of a quadratic function

  • Parabolic curve
• Quadratic function


  A function of degree 2 that can be written in the general form f(x) = ax^2 + bx + c where a, b, and c are real numbers and a ≠ 0
• Quadratic functions can be modelled by blocks
• The sequence of blocks models a quadratic function because the first differences in y are different while the second differences in y are the same
• A quadratic function is a function whose defining equation can be written in the general form f(x) = ax^2 + bx + c
• Quadratic function


  A function whose defining equation can be written in the general form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a ≠ 0
• A function is quadratic if and only if the degree of the equation is 2
• a, b, c


  The coefficients in the general form of a quadratic function f(x) = ax^2 + bx + c
• Quadratic functions

  • f(x) = x^2 - 3
  • f(x) = 2x^2 - x + 5
  • f(x) = 1/2 x^2 - 5
  • f(x) = 2x^2
• Representing a quadratic function

  1. Choose small values or numbers for x

  2. Substitute each chosen values of x to the given equation to solve for the values of y

  3. Prepare the table of values

  4. Write the resulting values of y in the prepared table of values

  5. Plot each point in the cartesian plane and connect the points with a smooth curve
• The graph of a quadratic function is a smooth curved called a parabola
• Equal differences in the independent variable x


  Produce equal second differences in the dependent variable y
• When we obtain equal differences in the independent variable x that produce equal differences in the dependent variable y, the resulting values represent a quadratic function
• Representing quadratic function by table of values and sketching the graph

  1. Choose small values or numbers for x

  2. Substitute each chosen values of x to the given equation to solve for the values of y

  3. Prepare the table of values

  4. Write the resulting values of y in the prepared table of values

  5. Plot each point in the cartesian plane and connect the points with a smooth curve
• Quadratic function


  A function of the form f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a ≠ 0
• Quadratic functions


  • f(x) = x^2 - 2x + 2
  • f(x) = -x^2 + 2x
• When graphing two quadratic functions, use two different colors of pen to differentiate one graph from the other
• The rubric for evaluating the activity includes accuracy of the table of values, correctness of the graph, and analysis of the differences between the two graphs
• General form of a quadratic function

  f(x) = ax^2 + bx + c, where a, b, and c are real numbers and a ≠ 0
• An incomplete quadratic function is one that is not in the general form