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Examples For Section 3.1

Example 1

Put the given equation of a quadratic function in standard form in order to determine the location of the vertex of its graph (a parabola).  Also find its x-intercepts, y-intercept, the equation of its axis of symmetry, and use symmetry to find three additional points on the graph.  Give the domain and range of the function.

The axis of symmetry is shown as a broken blue line.

The graph of the function does not end at the two highest points plotted.  It keeps going "up and out" forever.  Thus the domain of the function is all real numbers.  This can also be deduced from the equation defining the function since in it you could substitute any real value for x and get a real value output for y.  Since the graph has an absolute low point at (1,-9), the vertex of the parabola, y cannot take any value less than -9.  It can take any y-value greater than or equal to -9.  Thus the range of the function is all values for y greater than or equal to -9.

 

Example 2

Put the given equation of a quadratic function in standard form in order to determine the location of the vertex of its graph (a parabola).  Also find its x-intercepts, y-intercept, the equation of its axis of symmetry, and use symmetry to find three additional points on the graph.  Give the domain and range of the function.

The axis of symmetry is shown as a broken blue line.

The graph of the function does not end at the two lowest points plotted.  It keeps going "down and out" forever.  Thus the domain of the function is all real numbers.  This can also be deduced from the equation defining the function since in it you could substitute any real value for x and get a real value output for y.  Since the graph has an absolute high point at (-2,27), the vertex of the parabola, y cannot take any value greater than 27.  It can take any y-value less than or equal to 27.  Thus the range of the function is all values for y less than or equal to 27.

 

Example 3

Write an equation in standard form of the parabola that has the same shape as the parabola given by the equation defining the quadratic function f but the vertex of this parabola is at (4,2).

 

          

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        Lane Vosbury, Math Chair, Seminole Community College   email:  vosburyl@scc-fl.edu

        This page was last updated on 10/08/08          Copyright 2002          webstats