Characteristics of quadratic functions

Lessons

• 1.
  Determining the Characteristics of a Quadratic Function Using Various Methods

  Determine the following characteristics of the quadratic function $y = -2x^2 + 4x + 6$:

  • Opening of the graph

  • $y-$intercept

  • $x-$intercept(s)

  • Vertex

  • Axis of symmetry

  • Domain

  • Range

  • Minimum/Maximum value

  a)

  Using factoring
  
  
  b)

  Using the quadratic formula
  
  
  c)

  Using completing the square
  
  
  d)

  Using the vertex formula
  
  

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• 2.
  From the graph of the parabola, determine the:
  • vertex
  • axis of symmetry
  • y-intercept
  • x-intercepts
  • domain
  • range
  • minimum/maximum value
  
  a)

  
  
  
  
  
  b)

  
  
  
  
  

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• 3.
  Identifying Characteristics of Quadratic function in General Form: $y = ax^2 + bx+c$
  $y = 2{x^2} - 12x + 10$ is a quadratic function in general form.
  
  i) Determine:
  • y-intercept
  • x-intercepts
  • vertex
  
  ii) Sketch the graph.
  

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• 4.
  Identifying Characteristics of Quadratic Functions in Vertex Form: $y = a(x-p)^2 + q$
  $y = 2{\left( {x - 3} \right)^2} - 8$ is a quadratic function in vertex form.
  
  i) Determine:
  • y-intercept
  • x-intercepts
  • vertex
  
  ii) Sketch the graph.
  

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