Parabolas
Find the vertex, focus, directrix, and focal width of the parabola.
1) x2 = 28y
A) Vertex: (0, 0); Focus: (0, 7); Directrix: y = -7; Focal width: 28
B) Vertex: (0, 0); Focus: (0, -7); Directrix: x = -7; Focal width: 112
C) Vertex: (0, 0); Focus: (7, 0); Directrix: x = 7; Focal width: 7
D) Vertex: (0, 0); Focus: (7, 0); Directrix: y = 7; Focal width: 112
2) - 1 2
x = y
40
A) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 40
B) Vertex: (0, 0); Focus: (-20, 0); Directrix: x = 10; Focal width: 160
C) Vertex: (0, 0); Focus: (0, 10); Directrix: y = -10; Focal width: 10
D) Vertex: (0, 0); Focus: (0, -10); Directrix: y = 10; Focal width: 160
3) x = 8y2
A) Vertex: (0, 0); Focus: 0, 1
1
; Directrix: y = - ; Focal width: 32
32
32
B) Vertex: (0, 0); Focus: 1
1
, 0 ; Directrix: x = ; Focal width: 32
32
32
C) Vertex: (0, 0); Focus: 1
1
, 0 ; Directrix: x = - ; Focal width: 0.13
8
8
D) Vertex: (0, 0); Focus: 1
1
, 0 ; Directrix: x = - ; Focal width: 0.13
32
32
4) y2 = 8x
A) Vertex: (0, 0); Focus: (0, 2); Directrix: y = -2; Focal width: 2
B) Vertex: (0, 0); Focus: (2, 0); Directrix: x = -2; Focal width: 8
C) Vertex: (0, 0); Focus: (2, 0); Directrix: x = -2; Focal width: 32
D) Vertex: (0, 0); Focus: (2, 2); Directrix: x = 2; Focal width: 32
5) (y - 8)2 = 16(x - 2)
A) Vertex: (2, 8); Focus: (6, 8); Directrix: x = -2; Focal width: 16
B) Vertex: (8, 2); Focus: (8, 18; Directrix: y = -14; Focal width: 16
C) Vertex: (2, 8); Focus: (18, 8); Directrix: x = -14; Focal width: 16
D) Vertex: (8, 2); Focus: (8, 6); Directrix: y = -2; Focal width: 4
6) (x - 8)2 = 16(y - 6)
A) Vertex: (6, 8); Focus: (10, 8); Directrix: x = 4; Focal width: 4
B) Vertex: (6, 8); Focus: (22, 8); Directrix: x = -8; Focal width: 16
C) Vertex: (8, 6); Focus: (8, 10); Directrix: y = 2; Focal width: 16
D) Vertex: (-8, -6); Focus: (-8, 10); Directrix: y = -22; Focal width: 16
Find the standard form of the equation of the parabola.
7) Vertex at the origin, focus at (0, 9)
1
A) y = x2
B) y2 = 36x
9
C) y2 = 9x
D) y = 1 2
x
36
PreCalculus
8) Focus at (0, 4), directrix y = -4
1
B) y = x2
4
A) y2 = 4x
C) y = 1 2
x
16
D) y2 = 16x
9) Vertex at the origin, focus at (2, 0)
1
B) x = y2
8
1
C) y = x2
8
D) x2 = 8y
C) y2 = -8x
1
D) y = - x2
8
11) Focus at (-3, 2), directrix x = -11
A) (y - 2)2 = 16(x + 3)
B) (x + 3)2 = 16(y - 2)
C) (x - 2)2 = 16(y + 7)
D) (y - 2)2 = 16(x + 7)
12) Focus at (6, -2), directrix y = -8
A) (y + 2)2 = 12(x - 6)
B) (x - 6)2 = 12(y + 2)
C) (x - 6)2 = 12(y + 5)
D) (x + 2)2 = 12(y + 5)
13) Vertex at the origin, opens to the right, focal width = 14
A) y2 = 14x
B) y2 = -14x
C) x2 = 14y
D) y2 = 3.5x
A) y2 = 8x
10) Focus at (-2, 0), directrix x = 2
1
B) -8y = x2
A) x = - y2
8
Graph the parabola.
14) 8y = x2
y
10
5
-10
-5
5
10
x
-5
-10
Calin M. Agut - 2012
PreCalculus
15) 4y = -x2
y
10
5
-10
-5
5
10
x
10
x
10
x
-5
-10
16) (y - 3)2 = 4(x + 2)
y
10
-10
-10
17) y = -6(x + 4)2 + 4
y
10
5
-10
-5
5
-5
-10
Calin M. Agut - 2012
PreCalculus
4
18) y = (x + 4)2 - 3
7
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
19) x = -3(y + 2)2 - 1
y
10
5
-10
-5
-5
-10
Find the vertex, the focus, and the directrix of the parabola.
20) x2 + 2x - 8y - 39 = 0
A) Vertex: -1, 1 ; Focus: (-1, 3); Directrix: y = 13
B) Vertex: -1, - 5 ; Focus: (-1, -3); Directrix: y = -7
C) Vertex: -1, - 4 ; Focus: (-1, -7); Directrix: y = -3
41
39
; Focus: (-1, 3); Directrix: y = - D) Vertex: -1, - 8
8
21) 3x2 - 30x - y + 77 = 0
24
23
25
A) Vertex: 5, ; Focus: 5, ; Directrix: x = 83
12
12
C) Vertex: 5, 5 ; Focus: (5, 5); Directrix: x = -1
B) Vertex: 5, 2 ; Focus: 5, D) Vertex: 5, 25
23
; Directrix: y = 12
12
19
; Focus: (5, 14); Directrix: x = 10
2
22) y2 - 8x - 6y + 17 = 0
A) Vertex: 5, 1 ; Focus: (9, 1); Directrix: y = 7
C) Vertex: - 4, 3 ; Focus: 9
7
, 3 ; Directrix: y = 8
8
B) Vertex: 0, 1 ; Focus: (-1, 1); Directrix: y = 3
D) Vertex: 1, 3 ; Focus: (3, 3); Directrix: x = -1
Calin M. Agut - 2012
Answer Key
Testname: 10_PARABOLAS
1) A
2) A
3) D
4) B
5) A
6) C
7) D
8) C
9) B
10) A
11) D
12) C
13) A
14)
y
10
5
-10
-5
5
10
x
5
10
x
-5
-10
15)
y
10
5
-10
-5
-5
-10
Calin M. Agut - 2012
Answer Key
Testname: 10_PARABOLAS
16)
y
10
10
x
5
10
x
5
10
x
-10
-10
17)
y
10
5
-10
-5
-5
-10
18)
y
10
5
-10
-5
-5
-10
Calin M. Agut - 2012
Answer Key
Testname: 10_PARABOLAS
19)
y
10
5
-10
-5
5
10
x
-5
-10
20) B
21) B
22) D
Calin M. Agut - 2012