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.**

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

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** ****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.**

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

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**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:**

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**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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**return
to Brooke's EMAT6680
page**