9.2 Parabolas (Day 1)
State whether the graph of the equation is a parabola.
1. y = 2x 2 + 3
2. y + x2 = 7
3. y = 3x + 9
4. y = 6x2 – x + 3
5. y2 = 5
Standard equation of a parabola with vertex at (0, 0)
Equation
Focus
Directrix
x2 = 4py
y2 = 4px
(0, p)
(p 0)
y = -p
x = -p
Axis of
Symmetry
x=0
y=0
Opens
Vertically
Horizontally
NOTE: The directrix is ALWAYS perpendicular to the axis of symmetry‼!
Identify the focus and the directrix of the parabola:
𝟑
1. 𝒙 = 𝒚𝟐
2. Y = ½ x2
𝟒
Graph the equation. Identify the focus and directrix.
1. y 2 =- 3x
2. x 2 = 4y
Write the standard form of the equation of the parabola with the given focus
and vertex at (0. 0).
1. F (0, 3)
2.
F (-1, 0)
Write the standard form of the equation of the parabola with the given directrix
and vertex at (0, 0).
3. y = 2
4.
x = -3
A microphone has a parabolic reflector around it to capture sound. The
microphone is placed at the focus of the parabola to reflect as much sound as
possible.
a. Write an equation for the cross section
of the reflector.
(Scale of 2)
(10, 5)
b. How high is the microphone above the
vertex?
9.2 Parabolas (Day 2)
General Form of a Parabola:
Form of Equation
(y - k) 2 = 4p (x – h) (x – h) 2 = 4p (y – k) ( x + 3)2 = 8(y – 4)
Vertex
Axis of Symmetry
Focus
Directrix
Direction of Opening
1.
Graph (x – 1) 2 = 2(y – 3).
Find the
Vertex
Focus
Directrix
2. Graph 4y2 + 4y – 4x – 16 = 0
Find the
Vertex
Focus
Directrix
Find an equation for the parabola satisfying the given conditions.
3. Focus (-2, -1); directrix y = 3
4. Focus (4, 1); vertex (7, 1)
5. Vertex (1, -3); directrix x = 5