Explorations of the Parabola

By Brooke Norman

 

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Ever wondered what happens to a parabola when you change a variable?

We are going to explore the graph of 

 

 

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We will first explore the graphs when a is a positive number.

                        

                                      

 

 

                  

          

 

 

 

 

 

As you notice, as a increases, the parabolas are concave up and become skinnier. 

 

 

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 We will now explore the graphs when a is a negative number.           

 

                           

                 

 

 

                            

  

 

 

 

As you notice, as a decreases, the parabolas are concave down and become skinnier.

 

 

 

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Lastly, we will explore the graphs as a is a fraction between 0 and 1.

 

 

As you can see, as the fraction becomes smaller, the parabola becomes wider, closer and closer to appearing to be a straight line. 

 

 

 

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In conclusion:

 

If a >0, the parabola will open upward

If a is <0, the parabola will open downward.

If a is =0, the parabola is the x-axis.

As |a| becomes larger, the parabola becomes skinnier.

As |a| becomes smaller, the parabola becomes wider.

 

 

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