Aim #53-54: How do we analyze the graph of a parabola?
HW Packet Due Friday 2/3
Quiz (Aims 52-54) Friday 2/3
Do Now:
Determine the equation of the axis of symmetry of the
following parabola. Then determine the vertex.
Aim #53-54: How do we analyze the graph of a parabola?
HW Packet Due Friday 2/3
Quiz (Aims 52-54) Friday 2/3
DO NOW
Write the equation of a parabola with vertex at (0, 0)
and focus at (3, 0).
Parabola
A parabola is the collection of all points P in the plane that are the
same distance from a fixed point F as they are from a fixed line D.
The point F is called the focus of the parabola, and the line D is its
directrix.
As a result, a parabola is the set of points P for which
d(F, P) = d( P, D);
d = distance
p
p
Since the vertex is a point on
the parabola it must satisfy
the definition.
d(F,V) = d(V,D)
We will call this distance p.
General Forms of Parabolas
If the vertex is at (0,0) Vertical axis: Horizontal axis:
Find the vertex, focus, and directrix.
y2 = 16x
To graph this parabola, it is helpful to find the points
directly above/below or along side the focus, using
either the x or y coordinate of focus.
Find the vertex, focus, directrix, and
two other points on the parabola.
x2 = 6y
Write the equation of the parabola with
vertex (-2,3) and a focus at (0,3). Also, state
the equation of the directrix and sketch a
graph of the equation.
Write the equation of a parabola with focus at (0, 4) and
directrix the line y = -4. Also state two additional points
on the parabola.
Find the vertex, focus, directrix, two other points on the
parabola, and sketch the following:
Find the focus, directrix, and sketch the following:
Write the equation of a parabola with vertex at (0, 0)
and directrix the line x = 3/4.
Find the focus, directrix, and sketch the following:
2
y + 2y = -x + 1
Find the equation of the parabola with a focus at
(2,4) and directrix the line x = -4. Graph the
equation.
PRACTICE
Find the vertex, focus, directrix, and sketch the following:
y2 = ­8x
x2 = ­12y