RWA #1: Unit M Concept 4:Graphing parabolas given equation

RWA Conic Section: Parabola

1. Definition: "The set of all points the same distance from a point and a line"

2.Properties:  

•                    Algebraically:  

•                            Formula/Equation: 

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•                        Graphically: The graph consist of many key factors that belong to a parabola. The center of the parabola is called the VERTEX and it focuses around the FOCUS. The AXIS OF SYMMETRY goes straight through the parabola, which is also perpendicular to the DIRECTRIX.  

•  The directrix is the line outside the parabola that you can identify by subtracting the value from the vertex (h or k) by p. The notation for the directrix is x=# and y=#. "p" is a point that is determined by setting the term outside of the non-squared portion of the formula equal to 4p and solving. "p" is the value that determines how far away the focus and the directrix are from the vertex.To put the equation into standard form,  complete the square and be sure that only one term is squared. If the x term of the equation is squared and the value of p is negative the graph will go down and if the value of p is positive the graph will go up. In contrast,  if the y term is squared and the value of p is positive the graph will go right, if p is negative the graph will go left. The vertex is an ordered pair that is the center of the parabola. The values of h,k is the vertex as an ordered pair. Remember that h always goes with x and y always goes with k. 
• The axis of symmetry is a line that lies in the middle of the parabola that is written as x=#  or y=#.The value for the axis of symmetry is the number from the vertex that isn't changing.  The focus is an ordered pair found inside the parabola that is identified by adding the value of p with the term that isn't changing (h or k).
• The distance that the focus is from the vertex determines how skinny or how fat the parabola is. In addition, the distance from the focus to any point on the parabola to the directrix is always equal and that is called the eccentricity. A parabola's eccentricity is equal to 1 which is why the two distances are equal.

4. RWA: Parabolic Antennas 

The  Parabolic Antennas are constructed as parabolas because that allows any sound and waves to hit it faster and easier than as a regular square would. he shape of he Parabola is used to attract waves. 

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