The document discusses parabolas including their parts, graphs, and equations. It defines a parabola as the locus of points where the distance to the focus is equal to the distance to the directrix. The parts of a parabola include the vertex, focus, directrix, axis of symmetry, and latus rectum. The document outlines the graphs of parabolas with the vertex at the origin or at a point (h,k), and opening in different directions. It notes equations will be provided for parabolas with the vertex at the origin or (h,k), but does not show the actual equations.

1. Lecture #6
• Parabola
• Parts of Parabola
• Equations of Parabola with center at origin
• Equations of parabola with center at (h, k)
• Graph of Parabola

2. PARABOLA
 Locus of points such that the distance from a point to
the focus is equal to the distance from the same point
and the directrix.

3. PARTS OF PARABOLA
 Vertex – sharpest turn point of the parabola. (represented
by V)
 Focus – a point which is used to determine or define the
parabola. (represented by F)
 Latus Rectum – a line passing through the
focus, perpendicular to the axis of symmetry, and it has
two endpoints.
 Directrix – a line perpendicular to axis of symmetry
(represented by D)
 Axis of symmetry – a line that divides the parabola in
half
 Eccentricity – the eccentricity of the parabola is always
equal to one. (represented by e)

4. PARTS OF PARABOLA

5. GRAPHS OF PARABOLA
 The graph of parabola if the vertex is at the
origin, and opens to the right,

6.  The graph of parabola if the vertex is at the
origin, and opens to the left,

7.  The graph of parabola if the vertex is at the
origin, and opens upward,

8.  The graph of parabola if the vertex is at the
origin, and opens downward,

9.  The graph of parabola if the vertex is at (h, k) , and
opens to the right,

10.  The graph of parabola if the vertex is at (h, k)
, and opens to the left,

11.  The graph of parabola if the vertex is at (h, k) ,
and opens upward,

12.  The graph of parabola if the vertex is at (h, k) , and
opens downward,

13. EQUATIONS OF PARABOLA
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22. FORMULAS
VERTEX AT
(0, 0 )
FOCUS DIRECTRIX
ENDS OF
LATUS
RECTUM
LENGTH
OF LATUS
RECTUM
EQUATION
OF
PARABOLA
RIGHT
LEFT
UPWARD
DOWNWARD

23. FORMULAS
VERTEX
AT (h, k)
FOCUS DIRECTRIX
ENDS OF
LATUS
RECTUM
LENGTH
OFLATU
S
RECTUM
EQUATION OF PARABOLA
RIGHT
LEFT
UPWARD
DOWNWARD

24. Sample Problem
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