MODULE 10

• DISCIPLINE • GOOD TASTE • EXCELLENCE
• Writer: Gemma Y. Bandoquillo
• Cover Illustrator: Joel J. Estudillo
• MATHEMATICS Quarter 1: Module 10 Graph of Quadratic Function
• Department of Education National Capital Region SCHOOLS DIVISION OFFICE MARIKINA CITY
• Quadratic function


  Graph of the function is called a parabola
• Parabola


  • Can be described as trajectories of a bouncing ball
  • Incorporated into structures like parabolic reflectors that form the base of satellite dishes and car headlights
  • Used in business to forecast profit and loss
  • Famous structures like churches, mosques, monuments, bridges, and buildings around the world have parabolic arches
  • Most objects we use every day like clocks, mirrors, cars, do not exist if they have no application of quadratic function
• Graphing Quadratic Function

  1. Make a table of values

  2. Draw the graph on the Cartesian Plane
• Domain


  The set of all real numbers, or x = -5,-4,-3,-2,-1,0,1
• Range


  If a > 0, the range is {y/y ≥ k} or [k, +∞)<|>If a < 0, the range is {y/y ≤ k} or (-∞,k]
• Vertex


  The turning point of the parabola, either the lowest or highest point
• Axis of symmetry


  The line that divides the parabola into two equal halves
• 1. intercepts


  The points where the parabola crosses the x-axis
• 1. intercept


  The point where the parabola crosses the y-axis
• To determine the Domain, Range, Axis of Symmetry, Vertex and Opening of the Parabola, let us consider the graphs of y = x^2 + 4x - 5 and y = -x^2 - 4x + 5
• Axis of symmetry


  A line which divides the parabola into two parts such that one-half of the graph is a reflection of the other half
• Quadratic function in the form y = a(x - h)^2 + k


  The line x = h is the axis of symmetry
• 1. intercepts


  The points (or their x-coordinates) where the curve crosses the x-axis. They are the zeros of the function or the roots of ax^2 + bx + c = 0
• 1. intercepts


  The points (or their y-coordinates) where the curve crosses the y-axis. For the parabola y = ax^2 + bx + c, there is exactly one y-intercept obtained by setting x to zero: y = c
• To determine the Domain, Range, Axis of Symmetry, Vertex and Opening of the Parabola


  Consider the graphs of y = x^2 + 4x - 5 and y = -x^2 - 4x + 5
• Vertex form


  y = -a(x - h)^2 + k
• Domain


  The set of real numbers or {x|x∈R}
• Range


  If a < 0, then the range is {y|y ≤ k} or (-∞, k]
• Vertex


  The point (h, k)
• Axis of symmetry


  x = h
• 1. intercept


  y = c
• To find x-intercepts

  Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
• If a < 0, then the function has a maximum point and k determines the maximum value
• Vertex form


  y = a(x - h)^2 + k
• y = (x + 5)^2 - 9

  • x = -8, -7, -6, -5, -4, -3, -2

  y = 0, -5, -8, -9, -8, -5, 0
• The graph of y = (x + 5)^2 - 9 is a parabola
• The parabolic path of the ball is traced by the graph
• Husband, a member of Azkal contributed 2 goals
• Parabolic path of the ball

  1. Traced by the graph below

  2. When he kicked the ball on the ground
• RUBRICS for checking and scoring:
• ACCURACY

  • Answered 5 questions correctly
  • Answered 4 questions correctly
  • Answered 3 questions correctly
  • Answered 2 questions correctly
  • Answered 1 question correctly
• COMPLETION

  • All 5 of the assigned works are completed
  • 4 of the assigned works are completed
  • 3 of the assigned works are completed
  • 2 of the assigned works are completed
  • Only 1 of the assigned work is completed
• NEATNESS


  • STRONGLY OBSERVED (10)
  • FAIRLY OBSERVED (6)
  • Needs Improvement (4)
• SUMMATIVE TEST
• Answers

  • 𝑦 = 2(𝑥 − 2)2 − 5
  • 𝑦 = 2(𝑥 − 2)2 + 5
  • 𝑦 = 2(𝑥 + 2)2 − 5
  • 𝑦 = 2(𝑥 + 2)2 + 5