RWA #1- Unit M Conceot 4-6: Parabola

1) Definition: The set of all points that are equidistant from the focus to the directrix.

y2 = 4ax

y2 = -4ax

x2 = 4ay

x2 = -4ay

To define a parabola it is important you look at its equation. As we can see above, in the first two example, when the y is squared, the graph goes to left and right. Having p positive or negative decided which direction it will go. For the other two equations algebraically, the x is squared and p also change signs. This transfer graphically because depending on the sign of p it will either open up or down.

 As we can see above, in the first two example, when the y is squared, the graph goes to left and right. Having p positive or negative decided which direction it will go. For the other two equations algebraically, the x is squared and p also change signs. This transfer graphically because depending on the sign of p it will either open up or down.

The key parts of the parabola are the directrix, p value, axis of symmetry, vertex, and focus. The axis of symmetry is a line that cuts in between the parabola, perpendicular to the axis of symmetry is the directrix. The focus is p, which is a point inside the parabola. The distance from p to a point in the graph should be the same from that point on the graph to the directrix. The p-value is also important because if p is less than one the graph will look skinny if it is greater than 1 it will become fatter.

Link to parabola explanation: ( http://youtu.be/-1MzoyzWxo4 )

<iframe width="420" height="315" src="//www.youtube.com/embed/-1MzoyzWxo4" frameborder="0" allowfullscreen></iframe>

3. Parabolas are everywhere, they are essentially a curved line. Kicking a soccer ball is a parabola. The vertex of the path of the soccer ball would be at the point where the soccerball is highest. One peal world event where parabolas are used are in the reflectors in your flash light. “rays emanating from the focus point will reflect off the parabola parallel to the axis of symmetry.” (http://youtu.be/Djnwlj6OG9k)

4. works cited

http://youtu.be/Djnwlj6OG9k( flashlight RWA)

http://www.mathsisfun.com/geometry/parabola.html (picture of parabola)