Contents of this Precalculus episode:

Completing the square, Internal transformation, external transformation, reflection about x axis, reflection about y axis.

Text of slideshow

We will try graphing this function based on the transformations shown in the previous slides.

In order to decide which transformations was this function a victim of, first we will have to do a very funny thing with it.

We call this procedure “completing the square”. We will need it many times in the future, so let’s get it over with.

It boils down to these two identities:

This time we are going to use them in this direction.

We will look at the function over and over, until we recognize one of the identities.

Let’s see, what could be the value of b?

Well, this:

And now we can graph this, if we remember the previous slides.

Let’s see this one, too:

Now it is time to discuss some new functions.

In the next slideshow there come the exponential functions.

# The art of “completing the square”

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Completing the square, Internal transformation, external transformation, reflection about x axis, reflection about y axis.

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Precalculus episode