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Stephani Eckelkamp

 

A More In Depth Look at the Parabola

ax2 + bx + c = y

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All of these equations pass through the point y = 1.  We can conclude that the constant c will effect where the parabola crosses the y axis.

 

 

 

 

In the assignment ÒParabola: Friend of FoeÓ we can see graphs when b and c are constant.  b = 1 and c = 0.  Below is an example of some graphs with a changing.

 

 

 

 

 

 

 

 

                        Link to ÒParabola:  Friend or FoeÓ

 

 

 

 

 

 

 

                                       

 

 

 

 

                                                                            

 

 

 

                                                                            

                                                                                                                        The equation of the parabolas to the left are in the form of x2 + x + c = y,           where c is a constant.  The values for c in the graph are -3, -2, -1, 0, 1,             and 2, and 3.  From the graph and the equation we can conclude that            the constant c changes where the parabola crosses the y axis.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

           

Now that we know how the constants effect the parabola, let us look at the first graph again.

 

 

 

 

 

 

  

 

 

 

 

 

 

By looking at the graph above we can see that x2 +2x + 1 = y and x2 – 2x + 1 = y.  Both of these graphs cross the x axis at -1 and 1.  We can also see the all of the above graphs cross the y axis at 1.  By using this information we can find the roots of an inverted parabola that crosses through all the vertices of the above equations. 

 

 

The black, inverted parabolaÕs equation is:

 

x2 – 1 = y

 

As we can see, this inverted parabola has roots at -1 and 1, and has a vertex on the y axis at 1. 

 

 

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