parabolas and circles notes - mr. ehrman's page · parabolas and circles notes name_____...
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Pre Calculus
Parabolas and Circles Notes
Name___________________________________
Date________________ Period____
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-1-
Use the information provided to write the vertex form equation of each parabola. Identify thevertex, focus, directrix, y-intercept, and x-intercepts of each. Then sketch the graph.
1) y = 4x2 + 72x + 326
x
y
-12 -10 -8 -6 -4 -2 2
2
4
6
8
10
12
14
16
18
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-2-
2) x = -1
4y2 - y + 9
x
y
-1 1 2 3 4 5 6 7 8 9 10 11
-10
-8
-6
-4
-2
2
4
6
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-3-
Use the information provided to write the vertex form equation of each parabola.
3) y = -1
4x2 -
5
2x -
61
4
4) x = 2y2 + 32y + 133
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-4-
Use the information provided to write the vertex form equation of each parabola. Identify thevertex, focus, directrix, y-intercept, and x-intercepts of each.
5) y = 1
3x2 - 3x +
14
3
6) x = -2y2 + 22y - 60
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-5-
Use the information provided to write the standard form equation of each circle.
7) Three points on the circle: (-13, -10), (-3, -10), and (-15, 2)
Use the information provided to write the vertex form equation of each parabola.
8) Vertex: (-3, 2), Directrix: y = 47
24
9) Focus: (-11, -4), Directrix: x = -9
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Worksheet by Kuta Software LLC
Pre Calculus
Parabolas and Circles Notes
Name___________________________________
Date________________ Period____
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-1-
Use the information provided to write the vertex form equation of each parabola. Identify thevertex, focus, directrix, y-intercept, and x-intercepts of each. Then sketch the graph.
1) y = 4x2 + 72x + 326
x
y
-12 -10 -8 -6 -4 -2 2
2
4
6
8
10
12
14
16
18
y - 2 = 4(x + 9)2
Vertex: (-9,2)No x-interceptsy-intercept (0,326)Focus: (-9, 33/16)
Directrix y = 31
16
x
y
-12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1
-1
1
2
3
4
5
6
7
8
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-2-
2) x = -1
4y2 - y + 9
x
y
-1 1 2 3 4 5 6 7 8 9 10 11
-10
-8
-6
-4
-2
2
4
6
x - 10 = -1
4(y + 2)2
Vertex: (10,-2)x-intercept: (9,0)y-intercept (0, -2±2 10)Focus: (9, -2)Directrix x = 11
x
y
-4 -2 2 4 6 8 10 12
-10
-8
-6
-4
-2
2
4
6
8
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-3-
Use the information provided to write the vertex form equation of each parabola.
3) y = -1
4x2 -
5
2x -
61
4
y = -1
4(x + 5)2
- 9
4) x = 2y2 + 32y + 133
x = 2(y + 8)2 + 5
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Worksheet by Kuta Software LLC
-4-
Use the information provided to write the vertex form equation of each parabola. Identify thevertex, focus, directrix, y-intercept, and x-intercepts of each.
5) y = 1
3x2 - 3x +
14
3
y + 25
12 =
1
3(x - 9
2)2
Vertex: (9
2, -
25
12)Focus: (9
2, -
4
3)Directrix: y = -
17
6
y-intercept: (0, 14
3 )x-intercept: (7, 0) and (2, 0)
6) x = -2y2 + 22y - 60 x - 1
2 = -2(y -
11
2 )2
Vertex: (1
2,
11
2 )Focus: (3
8,
11
2 )Directrix: x =
5
8y-intercept: (0, 5) and (0, 6)x-intercept: (-60, 0)
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-5-
Use the information provided to write the standard form equation of each circle.
7) Three points on the circle: (-13, -10), (-3, -10), and (-15, 2)
(x + 8)2 + (y + 3)2
= 74
Use the information provided to write the vertex form equation of each parabola.
8) Vertex: (-3, 2), Directrix: y = 47
24
y = 6(x + 3)2 + 2
9) Focus: (-11, -4), Directrix: x = -9
x = -1
4(y + 4)2
- 10