Parabola
Parabola
– The set of all points in the plane such that each point is the same distance from a
point F, called the focus, and line d, called the directrix. The graph of a quadratic function is a parabola.
Example
of how a parabola is used in real life. Many
antennas are shaped so that a cross section of the antenna is a parabola. This shape improves the ability of the antenna to
focus the signal that it is sending or receiving. The
sender or receiver for the antenna is located at a point called the focus of the parabolic
cross section. You can define a parabola
using this point and a line called the directix.
Equations
a parabola: y=a(x-h)2+k, also (y
= ax2 + bx + c )
Example:
Point (2,1) as the focus and the line y=5 as its directrix.
Step
1: Find
the vertex of the parabola. The vertex (h,k)
is at the midpoint of the line segment connecting the focus (2,1) and the point (2,5) on
the directrix (h,k) =
(2+2/2, 1+5/2) = (2,3) (midpoint formula used)
Step
2: Find
the value of c. Use the fact that the
directrix is the line y=k-c 5=3-c -2=c (sub 5 for y and 3 for k)
Step
3: Find
an equation of the parabola using the general form of an equation of a parabola that opens
up or down.
y-k=1/4c(x-h)^2
y-3=1/4(-2) (x-2)^2 (sub 2 for h, 3 for k, and
–2 for c)
y-3=-1/8(x-2)^2
An
equation to a parabola is y-3=-1/8(x-2)^2
Plot
the vertex and at least one other point. Use
symemetry to sketch the graph
http://edservices.aea7.k12.ia.us/edtech/teacherpages/jmbrown/
http://www.exploratorium.edu/snacks/parabolas.html
http://www.mste.uiuc.edu/dildine/sketches/parabola.htm
http://www.mste.uiuc.edu/dildine/sketches/parabolas.htm
http://www.krellinst.org/UCES/archive/resources/conics/node52.html
http://library.thinkquest.org/10030/6conicpa.htm
http://www.csun.edu/~math095/schedule/notes/mod11/Parabolas.html
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