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MODULE III VOCABULARY PART I

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MODULE II 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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MODULE II 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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MODULE II 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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MODULE II 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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MODULE II

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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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MODULE II

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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

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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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MODULE II

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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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MODULE II 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.

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Parabola The set of all points that are equidistant from a given point (focus) and a given line (directrix).

Parabola The set of all points that are equidistant from a given point (focus) and a given line (directrix).

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