Graphing Quadratic Functions Standard Form

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Graphing Quadratic Functions Standard Form

• It is assumed that you have already viewed the
  previous slide show titled
• Graphing Quadratic Functions Concept.

• A quadratic function in what we will call
  Standard Form is given by

• The summary of the Concept slide show is given
  again on the next page.

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SUMMARY
Vertex
Face Up
Face Down
Axis of symmetry
Narrow
Wide
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• One more thing is needed before sketching the
  graph of a quadratic function. A point is
  plotted to know just how narrow or how wide the
  graph is.

• When the graph is narrow, choose an x-value
  that is only one unit from the vertex.

• In the graph on the right, a good choice would
  be
• x 1

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• If the value x 2 were chosen, then the
  corresponding y-value would be off the graph.

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• When the graph is wide, choose an x-value that
  is more than one unit from the vertex.

• In the graph on the right, a good choice would
  be
• x 2 or x 3

• Note that x 1 would not be very helpful in
  determining just how wide the graph would be.

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SUMMARY
Choose a value for x 1 unit away from the vertex.
Choose a value for x more than 1 unit away from
the vertex
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• Example 1

Sketch the graph of the following function
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• Since the graph is narrow, find a point that is
  only 1 unit from the vertex.
• Try x 3.

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• Draw the right branch of the parabola using the
  vertex and the point (3,4).

• Now use symmetry to draw the left branch.

• Label the axis and important points.

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• Example 2

Sketch the graph of the following function
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• Since the graph is wide, find a point that is
  more than 1 unit from the vertex (-1,-2).

• This problem presents another challenge, which
  is to avoid fractions if possible.

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• Therefore, we want to meet two goals
• Select an x-value more than one unit to the right
  of the vertex (-1,-2).
• Avoid fractions.

• To meet goal 2, all that is needed is for the
  quantity that is squared to be divisible by 5.

• An x-value of 4 meets this condition, and also
  satisfies goal 1.

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• Draw the right branch of the parabola using the
  vertex and the point (4,-7).

• Now use symmetry to draw the left branch.

• Label the axis and important points.

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END OF PRESENTATION
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