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9.3: Parabolas
College Algebra/Pre-Calculus
Objectives:
Graph parabolas with vertices at the origin.
Write equations of parabolas in standard form.
Graph parabolas with vertices not at the origin.
Axis of Symmetry
Latus Rectum
Parts of a Parabola:
Latus Rectum – the line
segment through the focus and
perpendicular to the AOS and
parallel to the directrix
Focus – the point equidistant
from the parabola and directrix
A•
•
•B
Focus
Directrix – the line the points
are equidistant to
Directrix
Vertex
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Parabolas:
Vertical
Standard Form
(Vertex)
Vertex
Axis of Symmetry
Horizontal
= − + (h, k)
x=h
+ (h, k + )
Directrix
= − Length of the latus
rectum
(h, k)
y=k
Focus
Direction of
Opening
= − (h + , k)
a > 0 ; opens up
a < 0 ; opens down
a > 0 ; opens right
a < 0 ; opens left
= −
Parabolas:
Ex. 1: Write the standard form for each equation of a parabola.
State the vertex, focus and directrix.
a) = −12
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Parabolas:
Ex. 1: Write the standard form for each equation of a parabola.
State the vertex, focus and directrix.
b) = 8
Parabolas:
Ex. 1: Write the standard form for each equation of a parabola.
State the vertex, focus and directrix.
c) − 2 = 4 + 1
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Parabolas:
Ex. 1: Write the standard form for each equation of a parabola.
State the vertex, focus and directrix.
d) + 2 + 4 − 7 = 0
Parabolas:
Ex. 1: Write the standard form for each equation of a parabola.
State the vertex, focus and directrix.
e) + 2 + 12 − 23 = 0
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Parabolas:
Ex. 2: Find the standard form of the equation of each parabola
satisfying the given conditions.
a) Focus: (8, 0); Directrix: x = -8
Parabolas:
Ex. 2: Find the standard form of the equation of each parabola
satisfying the given conditions.
b) Focus: (-3, 4); Directrix: y = 2
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9.3: Parabolas
Practice Problems:
• Page 958: 6, 14, 18, 22,
28, 30, 36, 40, 44-48
evens
Timeline:
5th
Block:
• Thurs (4/2)
8th Block:
• 9.2 Quiz
• 10.1 Notes
• Mon (4/6)
• 9.3 Quiz
• 10.2 Notes
• Wed (4/8)
• 10.1 Quiz
• 10.3 Notes
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