Quadratic Functions and Their Properties

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Section 3.3 Quadratic Functions and Their
Properties
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Examples
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Parabolas
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• For the following quadratic functions, find x and
  y-intercepts, axis of symmetry, vertex, and
  finally graph the equation. State the domain and
  range.
• 1.
• 2.
• 3.
• 4.

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• If you cant factor a quadratic equation, then
  you will need the
• ____________________________
• to find the ______________.
• The formula is
• ________________________________

Quadratic formula
x-intercepts
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• For the following quadratic functions, find x and
  y-intercepts, axis of symmetry, vertex, and
  finally graph the equation. State the domain and
  range.
• 5.
• 6.

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• We have just looked at quadratic functions in the
  form . Quadratic function
  can also be in the form
• ______________________________
• where (h, k) is the vertex.

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Graphing a quadratic function
Vertically stretched
Vertically compressed
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• Example For the following quadratic function,
  find x and y-intercepts, axis of symmetry,
  vertex, and finally graph the equation. Also,
  state the domain and range.

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Example Find the equation of the following
parabola
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• Note This function is NOT is the form
• From page A47 of class text.
• Completing the square adjusts a quadratic
  equation so that it becomes a perfect square.
• The following are example of quadratic equations
  that are perfect squares.

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To complete the square on we
add and get the result
Start Add
Result
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• Now, we will continue with the example Graph
  
• by transformations.

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• Lets complete the square on
• if f(x) 0 to find the x-intercepts.

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