Properties and graphs 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

   1. Using factoring
   2. Using the quadratic formula
   3. Using completing the square
   4. Using the vertex formula
2. From the graph of the parabola, determine the:
   • vertex
   • axis of symmetry
   • y-intercept
   • x-intercepts
   • domain
   • range
   • minimum/maximum value
   
   1. 
      
      
   2. 
      
      
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.
   
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.