Introduction
to Parabola
• Aparabola is the graph of a
quadratic function.
• It is a U-shaped curve that
can open upward,
downward, left, or right.
• Real-life examples: satellite
dishes, car headlights,
suspension bridges.
• One ofnature's best
approximations to
parabolas is the path of
a projectile.
5.
• This discoveryby Galileo in the 17th century made it
possible for cannoneers to work out the kind of path
a cannonball would travel if it were hurtled through
the air at a specific angle.
6.
• The oppositeprinciple is used in
the giant mirrors in reflecting
telescopes and in antennas used
to collect light and radio waves
from outer space:
• ...the beam comes toward the
parabolic surface and is brought
into focus at the focal point.
7.
• Parabolas exhibitunusual and useful
reflective properties.
• If a light is placed at the focus of a
parabolic mirror, the light will be
reflected in rays parallel to its axis.
• In this way a straight beam of light is
formed.
• It is for this reason that parabolic
surfaces are used for headlamp
reflectors.
• The bulb is placed at the focus for the
high beam and in front of the focus for
the low beam.
8.
Key Parts
of a
Parabola
•Vertex – the turning point of
the parabola.
• Axis of Symmetry – line
dividing the parabola into two
equal parts.
• Focus – fixed point inside
parabola.
• Directrix – fixed line outside
parabola.
• Latus Rectum – line segment
through focus, perpendicular
to axis.
Graph
Features
• If a> 0 → parabola opens
upward (minimum point).
• If a < 0 → parabola opens
downward (maximum point).
• The axis of symmetry passes
through the vertex.
• The parabola is symmetric
about its axis.
Example
Problem
• Find theequation of the
parabola with vertex at (0,0)
and focus at (0,3).
• Solution:
Since vertex is at origin and
focus is (0,3), axis is vertical.
• Equation: x² = 4ay → x² = 12y.
17.
Example 2
)
5
(
)
2
(
12
1 2
y
x
What is the vertex? How does it open?
(-2 , 5) opens
down
Example 3
2
)
2
(
125
5
y
x
What is the vertex? How does it open?
(0 , 2) opens
right
