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Section 9.2: The Parabola
Instructor: Ms. Hoa Nguyen
(nguyen@scs.fsu.edu)
1
Parabola Deﬁnition
In Section 3.1, we have learned that the graph of a quadratic function is a parabola. In
this section, we will understand the relation between the geometry of the parabola and the
quadratic equation.
Deﬁnition of a Parabola
:
Given a line
D
(
directrix
) and a point
F
(
focus
) not on
D
, the set of all points
P
such
that
d
(
P,F
) =
d
(
P,D
) is called a
parabola
.
Note:
d
(
A,B
) denotes the distance from
A
to
B
:
d
(
A,B
) =
p
(
x
A

x
B
)
2
+ (
y
A

y
B
)
2
.
The line through the focus
F
and orthogonal (perpendicular) to the directrix D is called
the
axis of symmetry
of the parabola.
The point where the parabola intersects with its axis of symmetry is called the
vertex
V.
2
Find the Equation of the Parabola
Case 1: The directrix is vertical, and the vertex is at the origin (
a >
0
).
1
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View Full DocumentTable 1: Equations of a Parabola: The directrix is vertical, and the vertex is at the origin.
Directrix
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 Spring '11
 Nuegyen
 Geometry

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