parabola powerpoint debra schablik western governor’s university
TRANSCRIPT
Creation of a Parabola
A conic section is a curve formed by the intersection of a plane a double-napped cone
(Zoebel, 1997-2006)
Where are parabolas?(Internet Access is Required)
•They’re everywhere.
•Put arrow on icon and click.
•Click power point icon on task bar to continue with slide show after video is finished.
(Part 1-They’re Out There!!!, 2008)
The Axis of Symmetry
For parabolas that open up or down, the axis of symmetry is the line x = the x-coordinate of the vertex.
For parabolas that open right or left, the axis of symmetry is the line y = the y- coordinate of the vertex.
The Focus
The focus is an ordered pair (x,y), and is INSIDE the parabola and on the axis of symmetry.
The Directrix
The directrix is a line that is perpendicular to the axis of symmetry and is always OUTSIDE the parabola.
4p
4p is the number in front of the variable that has a coefficient of 1.
is the distance from the vertex to the focus and/or the distance from the vertex to the directrix.
p
Focal Chord
The focal chord, 2p, is measured from the focus and gives the true width of the parabola.
opens up, with vertex at origin, to get the focus, plot the point 2 units inside the parabola and on the axis of symmetry, thus the focus is .
4 8 2p p
( , )0 2
)2,0(
The directrix is perpendicular to the axis of symmetry and is also 2 units away from the vertex, so the equation of the directrix is
y 2
2y
( , ) 4 0
opens left, with the vertex at origin. To find the focus, plot the point 4 units inside the parabola and on the axis of symmetry, thus the focus is .
( , ) 4 0
xy 162
)0,4(
x 4
The directrix is perpendicular to the axis of symmetry and is also 4 units away from the vertex, so the equation of the directrix is
x 4
4x
From the graph, the vertex is at the origin, (0,0), and the directrix is 2 units away from the vertex.
The parabola opens up, so the equation is in form. Since p = 2 , the equation is
Example #2 Writing the equation of a parabola
x py2 4
p 2
yx )2(42
yx 82 (Larson, Boswell, Kanold & Stiff, 2005)
pyx 42
#10 Write the standard form of the equation of the parabola with the given focus or directrix with the vertex at (0,0). Focus
)3,0(
Since the focus has to be inside the parabola and lie on the axis of symmetry, this parabola opens up, and is the form
pyx 42 The distance p is the distance from the vertex to the focus, or in this case 3.
So the equation is
x y x y2 24 3 12 ( )
References
Zoebel, Edward A. (1997-2006) Retrieved April 13, 2008. Welcome to Zona Land
http://id.mind.net/~zona/mmts/miscellaneousMath/conicSections/para
bolaPic1.jpg
Larson, Ron, Laurie Boswel, Timothy Kanold and Lee Stif. (2005). Algebra 2. Evanston Illinois: McDougall Little.
They’re Out There! (n.d.) retrieved April 20 , 2008 from http://www.youtube.com/watch?v=pQHxjJxQCzI