Math Analysis: RWA#1: Unit M Concpet 4-6- Conic Sections in Real LIfe

1. Parabola- Set of all points equal distance from a focus and the directrix
2.Algebraically

Graphically

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The parabola has FOUR key features: vertex, directrix, focus, and the axis of symmetry. The vertex is the point at which the parabola starts. The directrix is a line outside the parabola that is perpendicular to the axis of symmetry. The axis of symmetry is a line that breaks the graph into two equal sections. The focus is the point inside the parabola. Lastly the distance from the focus to the vertex and the vertex to the directrix is the same and known as "p".
For graphing the Parabola you need to make sure the formula is in standard form. After you have done that you can find your parts you know what the vertex is it is (h,k). Then plot the focus which you should know is p by now and you plot it away from the vertex meaning it should be inside the parabola. To know if p is going up, down, left or right you need to know that when "p" is positive and the equation is x^2 it goes up, if "p" is positive and equation is y^2 it goes right, if "p" is negative and equation is x^2 it opens down, if "p" is negative and the equation is y^2 it opens left. the effect the focus does to the shape is the distance from the vertex to the Focus which determines how skinny or fat the parabola is going to be. The closer the focus is to the vertex the fatter the graph will be, the further away the focus is from the vertex the skinnier the graph will be.The eccentricity of the parabola is equal to 1 all the time.You then put in the directrix which is a line p units away from the vertex in the opposite direction of the focus. Then put in the axis of symmetry which is perpendicular to the directrix. Notice that the vertex and the focus are both going to be ordered pairs while the directrix and the axis of symmetry are going to be lines.
3. RWA

http://upload.wikimedia.org/wikipedia/commons/4/48/Headlight_lens_optics_schematic.png The cars headlights can be a great example of having a parabolic shape."The light is placed in the focus of a parabolic mirror, as the light travels and meets the mirror, it is reflected in lines parallel to the axis . This is why the light beam from the headlights of cars are so strong."( http://www3.ul.ie/~rynnet/swconics/UP.htm) source should be the vertex that bounces all of the dispersed lights from the reflector in a straight line straight forward.

"Parabolic reflector has the property that if a light source is placed at the focus of the reflector then the light rays will reflect from the reflector as rays that is parallel to the axis. To have a safe night drive you don't want all the light rays to be parallel to the axis. Some of the light must be aimed far down the road to the side upward for signs or bridges."(http://www.pleacher.com/mp/mlessons/calculus/appparab.html)

Here it talks more about the headlight and how you have to find the right vertex so that when it bounces all the rays stay straight.