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 ÒaÓ is a positive number.
We will now explore the graphs when ÒaÓ is a negative number.
As you notice, as ÒaÓ decreases, the parabolas are concave down and become skinnier.
Lastly, we will explore the graphs as ÒaÓ 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.
If ÒaÓ >0, the parabola will open upward
If ÒaÓ is <0, the parabola will open downward.
If ÒaÓ is =0, the parabola is the x-axis.
As Ò|a|Ó becomes larger, the parabola becomes skinnier.
As Ò|a|Ó becomes smaller, the parabola becomes wider.
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