MODULE 9

• General form of quadratic function

  𝑓(𝑥) = ��𝑥2 + ��𝑥 + 𝑐, where a, b, and c are real numbers, 𝑎 ≠ 0
• Standard form (Vertex form) of quadratic function

  𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘, where 𝑎 ≠ 0, and the point (ℎ, 𝑘) is called the vertex
• Transforming quadratic function from general form to standard form

  1. Factor 𝑎 in 𝑎𝑥2 + 𝑏𝑥

  2. Complete the square

  3. Simplify
• To find the vertex of f(x) = -2x^2 - x + 1


  1. Identify the values of a, b and c

  2. Substitute the values of a, b and c into the formulas h = -b/2a and k = (4ac - b^2)/4a

  3. Simplify
• The vertex of f(x) = -2x^2 - x + 1 is (-1/4, 9/8)
• Change the following quadratic functions to standard form

  Write the letter in the corresponding numbered spaces below to reveal the hidden word
• Quadratic functions to change to standard form

  • f(x) = x^2 - 2x + 5
  • f(x) = 2x^2 + 4x
  • f(x) = x^2 + 4x
  • f(x) = x^2 - 2x + 15
  • f(x) = x^2 - 6x + 5
  • f(x) = x^2 + 2x - 4
  • f(x) = -x^2 - 4x + 5
  • f(x) = -x^2 - 2x + 4
• Find the vertex of the following quadratic functions

  Choose the answer from the vertices at the table below and write the letter on the spaces provided before each number
• Quadratic functions to find the vertex

  • f(x) = x^2 - 2x + 5
  • f(x) = x^2 - 6x + 5
  • f(x) = -x^2 + 2x + 4
  • f(x) = 2x^2 + 4x
  • f(x) = x^2 + 2x - 4
• Vertices


  • (-1, -5)
  • (1, -5)
  • (-1, 4)
  • (3, -4)
  • (-1, -2)
  • (-3, 4)
  • (1, 4)
  • (1,5)
  • (1,2)
  • (1, -2)
• Two forms of quadratic functions

  General form<|>Standard/vertex form
• General form of quadratic function

  f(x) = ax^2 + bx + c
• Standard form of quadratic function

  f(x) = a(x - h)^2 + k
• Vertex of f(x) = -x^2 + 2


  (0, 2)
• Standard/vertex form of f(x) = x^2 - 6x + 8


  f(x) = (x - 3)^2 - 1
• Fill in the blanks for f(x) = x^2 + 10x + 15

  1. 10

  2. 25

  3. 10
• Fill in the blanks for f(x) = x^2 + 6x + 1

  1. 1

  2. 6

  3. 1

  4. -3

  5. -3
• The standard form of the quadratic function f(x) = a(x - h)^2 + k if a = 2, h = -2 and k = -2 is f(x) = 2(x + 2)^2 - 2
• The vertex form of f(x) = x^2 - 8x - 17 is f(x) = (x - 4)^2 - 33
• The vertex of the quadratic function in item number 1 is (-4, -33)
• The standard form of f(x) = x^2 + 4x - 6 is f(x) = (x + 2)^2 - 10
• The standard form of f(x) = x^2 - 4x - 7 is f(x) = (x - 2)^2 - 11
• General Form, Standard Form, Vertex

  • f(x) = 2x^2 - 1, (0, -1)
  • f(x) = x^2 - 6x + 9, f(x) = (x - 3)^2, (3, -9)
  • f(x) = x^2 - 6x, (3, -9)
  • f(x) = -x^2 + 2x, f(x) = -(x - 1)^2 + 1, (1, 1)
  • f(x) = -x^2 + 4x + 2, (2, 6)
• General Form, Standard Form and its Vertex


  • f(x) = x^2 + 6x + 10, f(x) = (x - 3)^2 + 1, (3, 1)
  • f(x) = x^2 - 6x + 10, f(x) = (x + 1)^2 - 3, (-1, -3)
  • f(x) = x^2 + 2x + 4, f(x) = (x + 1)^2 + 3, (-1, 3)
  • f(x) = x^2 + 2x - 2, f(x) = (x - 1)^2 + 3, (1,3)
  • f(x) = x^2 - 2x + 4, f(x) = (x + 3)^2 + 1, (-3, 1)
• Transforming the quadratic function from general form to standard form involves expanding the expression and simplifying
• To find the vertex, the values of a, b and c are substituted into the formulas h = -b/2a and k = (4ac - b^2)/4a
• If f(x) = x^2 - 6x + 11 is transformed to standard form, the resulting quadratic function is f(x) = (x - 3)^2 - 2
• Transform f(x) = -2(x + 6)^2 - 3 to general form


  1. Expand (x + 6)^2

  2. Apply distributive property

  3. Simplify
• The general form of f(x) = -2(x + 6)^2 - 3 is f(x) = -2x^2 - 24x - 75
• Transform f(x) = (x - 1/2)^2 + 1/3 to general form


  1. Expand (x - 1/2)^2

  2. Simplify
• The general form of f(x) = (x - 1/2)^2 + 1/3 is f(x) = x^2 - x + 7/12
• Corresponding general forms

  • f(x) = -x^2 - 4x - 5
  • f(x) = x^2 + 4x + 11/3
  • f(x) = x^2 - x + 5/4
  • f(x) = 2x^2 - 8x + 10
  • f(x) = -2x^2 - 4x - 1
  • f(x) = x^2 + 2x - 4
  • f(x) = 5x^2 + 20x + 20
  • f(x) = x^2 - 2x + 3/2
  • f(x) = -x^2 + 2x + 4
• Transform f(x) = (x + 2)^2 - 5 to general form


  1. Expand (x + 2)^2

  2. Simplify
• General form of f(x) = (x - 1/2)^2 + 1/3


  f(x) = x^2 - x + 7/12
• Determine the corresponding general form of each function

  Write the letter that corresponds to the correct answer on the space provided to decode the message
• f(x) = -2(x + 1)^2 + 1


  f(x) = -x^2 - 4x - 5
• f(x) = (x - 1)^2 + 1/2

  f(x) = x^2 - x + 5/4
• f(x) = -(x + 2)^2 - 1


  f(x) = 2x^2 - 8x + 10
• f(x) = (x - 1/2)^2 + 1

  f(x) = -2x^2 - 4x - 1
• f(x) = -(x - 1)^2 + 5


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