Explorations of the Parabola

By Brooke Norman

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

We are going to explore the graph of

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.

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.

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.

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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