VIDEO: Compressed or stretched parabola?

Parabolas can generally have three different forms: stretched, compressed or normal. First you should know what a stretched and what a compressed parabola is. A normal parabola generally has the form f (x) = x². If the parabola is narrower than a normal parabola, it is said to be stretched. However, if the parabola is flatter than a normal parabola, or if it is wider or wider than a normal parabola, it is compressed.

Use the vertex shape of a parabola to determine the shape

• If you also need to draw a parabola, it is always a good idea to convert the function into the vertex shape to reshapeif this is not already available.
• A parabola in vertex form generally has the function f (x) = a (x - d)² + e and thus the vertex S (d / e). The shape of the parabola is determined by the factor a.
• Is a² equals 1, then we have a normal parabola. If the amount of a or also a² is greater than 1, the parabola is stretched, i.e. it runs narrower or steeper than a normal parabola. If the amount of the factor is less than 1, it is a compressed parabola, i.e. it runs flatter or wider than a normal parabola.
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• Incidentally, if a is negative, the parabola is open downwards. If a is positive, the parabola is open upwards.


Reshape the functional term in the form of a vertex - this is how it works

In analysis it is often necessary to transform function terms in order to ...

Stretched or compressed parabola - this is how you recognize it

• The normal form of a parabola looks like this: f (x) = ax² + bx + c. Here you cannot immediately see the vertex, but you can see the general shape of the parabola. The factor a is responsible for this again.
• The following also applies here: If the amount corresponds to a factor of 1, it is a normal parabola. If the value of the factor a is greater than 1, the parabola is narrower, so there is an elongated parabola. If the amount of a is less than 1, the parabola is wider. There is consequently a compressed parabola.