MODULE III VOCABULARYPART I

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• Module III is called transformational geometry.

• In this module, we will be learning mathematically how to move figures around on a coordinate plane.

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• We can move many types of figures around on the coordinate plane.

• One of the first we will discuss is a parabola.

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• A parabola is the set of all points in the plane equidistant from a given focus and a given directrix.

• The lowest or highest point of the parabola is called the vertex.

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• A directrix is simply any horizontal line on a coordinate plane.

• A focus is simply a point NOT on the directrix.• The axis of symmetry is the line right down

the middle.

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• One of the standards I have to meet with you is that we must be able to construct a parabola, given a focus and a directrix.

• Follow along with me on the next slide as we do this.

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• You must also know how to write the equations for such graphs.

• The general formula for a parabola is…

4s(y – k) = (x – h)2

MODULE II• (h, k) is the vertex.• (x, y) is any point on the parabola.• s is the distance from the parabola from the

focus and the directrix.

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• The proper equation would be...

4s(y – k) = (x – h)2 4(1)(y – -2) = (x – 3)2

4(y + 2) = (x – 3)2

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• You will also need to do what we just did…backwards.

• Meaning, given the parabola you will have to identify the axis of symmetry, the vertex, the directrix and the focus.