HONORS ALGEBRA II
Section 10-2: Parabolas
Objectives:
To write the equation of a parabola and to graph parabolas
𝟏
Carefully and neatly graph 𝒚 = 𝟒 𝒙𝟐
Definition of Parabola: (In terms of a conic section)
 Set of all points in a plane that are the same distance from a fixed point
(
) and a fixed line (
).

The line perpendicular to the directrix containing the focus is the
_____________________________________________.

Distance from focus to vertex is ____________________________________.

c=
c=
Consider any parabola with equation y = ax2
If a > 0, then
If a < 0, then

the parabola opens

the parabola opens

the focus is at

the focus is at

the directrix is

the directrix is
Consider any parabola with equation x = ay2
If a > 0, then
If a < 0, then

the parabola opens

the parabola opens

the focus is at

the focus is at

the directrix is

the directrix is
Example: What is an equation of the parabola with vertex at the origin and focus at
(0, 2)?
1
Example: What are the focus and directrix of the parabola with equation 𝑦 = − 12 𝑥 2
Example: What is an equation of a parabola with vertex at the origin and directrix
x = 1.25?
Example: What are the vertex, focus, and directrix of the parabola with equation
x = 075y2?
Example: The parabolic solar reflector pictured has a depth of
2 feet at the center. How far from the vertex is the focus?
(What is the focal length?)
Recall: Vertex form of a parabola:
Translation form for parabolas as conics:
Recall: Completing the square:
Example: What are the vertex, focus, and directrix of the parabola with the equation
y = x2 – 4x + 8 ?
Example: What is an equation of the parabola with vertex (3, 7) and focus (5, 7)?