Precalculus
CS-3
PARABOLAS (PWL 9.1
AND
AM 6-5)
HOMEWORK #1
1)
Sketch the graph of y – 1 =
the indicated quantities.
-1
4
(x – 2)2. Identify
Orientation
2)
Sketch the graph of x + 1 =
indicated quantities.
1
8
(y – 4)2. Identify the
Orientation
Vertex
Focus
Vertex
Focus
EPFC
Directrix
EPFC
Directrix
Axis of Symmetry
MPH/CR 4/12
Axis of Symmetry
1
Precalculus
3)
Sketch the graph of y – 1 =
indicated quantities.
1
4
(x + 1)2. Identify the
Orientation
4)
Sketch the graph of x + 1 =
the indicated quantities.
-1
12
(y - 5)2. Identify
Orientation
Vertex
Focus
Vertex
Focus
EPFC
Directrix
EPFC
Directrix
Axis of Symmetry
MPH/CR 4/12
Axis of Symmetry
2
Precalculus
CS-3
PARABOLAS (PWL 9.1
AND
AM 6-5)
HOMEWORK #2
For each of the following parabolas, write the equation in standard form. Sketch the
parabola and identify the indicated quantities.
1)
y2 – 8x + 6y + 25 = 0
Standard Form ________________________
Orientation
__________________________
Vertex __________
Focus
_________
EPFC _______________________________
Directrix ____________________________
Axis of Symmetry
2)
x2 – 8x - 4y + 12 = 0
_____________________
Standard Form ________________________
Orientation
__________________________
Vertex __________
Focus
_________
EPFC _______________________________
Directrix ____________________________
Axis of Symmetry
MPH/CR 4/12
_____________________
3
Precalculus
3)
x2 + 2x - 12y - 23 = 0
Standard Form ________________________
Orientation
__________________________
Vertex __________
Focus
_________
EPFC _______________________________
Directrix ____________________________
Axis of Symmetry
4)
y2 + 4x + 2y + 13 = 0
_____________________
Standard Form ________________________
Orientation
__________________________
Vertex __________
Focus
_________
EPFC _______________________________
Directrix ____________________________
Axis of Symmetry
MPH/CR 4/12
_____________________
4
Precalculus
CS-3
PARABOLAS (PWL 9.1
AND
AM 6-5)
HOMEWORK #3
Write the equation of each of the parabolas described in standard form.
1)
The vertex is at (3, 2), and the focus is at (7, 2).
2)
The vertex has a directrix y = 3, and the vertex is (-1, 1).
3)
The vertex is at (1, -2), and the directrix has the equation x = 4.
4)
The focus is at (6, 3), and the directrix has the equation y = -3.
5)
The directrix has the equation x – 6 = 0, and the focus is located at (2, -3).
6)
The endpoints of the focal chord are (7, 1) and (-1, 1), and “p” is positive.
7)
The EPFC are located at (3, 8) and (3, 0), and “p” is negative.
8)
The axis of symmetry is parallel to the y-axis, and the vertex is located at (3, -3).
The parabola contains the point (-4, 3).
9)
The axis of symmetry is parallel to the x-axis, and the vertex is (-2, 1). The
parabola contains the point (-4, -3).
10) The endpoints of the focal chord are (3, 1) and (3, 5), and the focus is to the right
of the vertex.
MPH/CR 4/12
5