Summary notes on the topic discussions on the definition, properties, illustration, graphs, and computation about the Parabola. Includes sample problem and graph illustration with a suggested answers. An assessment of learning about the topic is also provided with an answer.
, Parabola, open curve, a conic section produced by the intersection of a right circular cone and a
plane parallel to an element of the cone. As a plane curve, it may be defined as the path (locus) of
a point moving so that its distance from a fixed line (the directrix) is equal to its distance from a
fixed point (the focus). The parabola is the path, neglecting air resistance and rotational effects, of
a projectile thrown outward into the air.
The parabolic shape also is seen in certain bridges, either as arches, or in the case of a suspension
bridge, as the shape assumed by the main cable, if one assumes the weight of the vertical cables is
small compared to the weight of the roadway they support.
A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its
side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.
For a parabola whose axis is the x-axis and with vertex at the origin, the equation is y2= 2px, in
which p is the distance between the directrix and the focus. f(x) = y= ax2 + bx + c
When you kick a soccer ball (or shoot an arrow, fire a missile or throw a stone) it arcs up into the
air and comes down again ...
... following the path of a parabola!
(Except for how the air affects it.)
Parabola Examples:
Example 1: Consider an equation y = 3x2 - 6x + 5. For this parabola, a = 3, b = -6
and c = 5. Here is the graph of the given quadratic equation, which is a parabola.
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