RWA#1: Unit M Concept 4: Parabolas in Real Life

1. Parabola: "The set of all points the same distance from a point and a line." The point is called the focus and the line is called the directrix. (http://www.lessonpaths.com/learn/i/unit-m-conic-section-applets/parabola-drawn-from-definition-geogebra-dynamic-worksheet)

Here is a good introduction video to parabolas:

2.  Algebraically, the equation of a parabola is (x-h)^2=4p(y-k) or (y-k)^2=4p(x-h). The parabola is a U shape and will open left, right, up, or down depending on its equation.  The values in the equation can tell us which way the parabola is facing. If x is squared and p is positive, then it opens up. If y is squared and p is positive, then it opens to the right. If x is squared and p is negative, then it opens down.  And, lastly, if y is squared and p is negative, then the graph opens left.
        Moreover, some of its key points include: two points, a vertex (h,k) and a focus, and two lines, the axis of symmetry and the directrix.  The focus is always on the inside of the parabola and is "p" units from the vertex.  The directrix is a dotted line behind the parabola that is also "p" units from the vertex. Finally, the axis of symmetry is the dotted line the vertex and focus are resting on, and it also splits the parabola in half. Also, it is important to remember that the directrix and axis of symmetry are perpendicular.
If you want this explained in more detail, this website is a great resource:
http://www.purplemath.com/modules/parabola.htm

3. Satellite Dishes

Photo: http://i34.photobucket.com/albums/d129/coconut11/parabolicdish.jpg

Satellite dishes are great examples of everyday parabolas. They are created using the unique parabolic shape, so they can transmit and capture signals to and from a specific broadcast source. The shape of the satellite dish allows it to focus the signals hitting the dish to a specific point, the feedhorn or the focus. When the transmission signal focuses on the feedhorn, it broadcasts your favorite shows on your television. ^_^

4. References
http://www.lessonpaths.com/learn/i/unit-m-conic-section-applets/parabola-drawn-from-definition-geogebra-dynamic-worksheet
http://www.purplemath.com/modules/parabola.htm
http://electronics.howstuffworks.com/satellite-tv6.htm
http://www.youtube.com/watch?v=fV9YuF__fM4
http://i34.photobucket.com/albums/d129/coconut11/parabolicdish.jpg