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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Vertex Form of Parabolas
Use the information provided to write the vertex form equation of each parabola.
1)
y =
x
2
+ 16
x + 71 2)
y =
x
2
− 2
x − 5
3)
y =
−
x
2
− 14
x − 59 4)
y =
2
x
2
+ 36
x + 170
5)
y =
x
2
− 12
x + 46 6)
y =
x
2
+ 4
x
7)
y =
x
2
− 6
x + 5 8)
y =
(
x + 5
)(
x + 4
)
9)
1
2
(
y + 4
)
=
(
x − 7
)
2
10)
6
x
2
+ 12
x +
y + 13 = 0
11)
162
x + 731 =
−
y − 9
x
2
12)
x
2
− 12
x +
y + 40 = 0
13)
y =
x
2
+ 10
x + 33
14)
y + 6 =
(
x + 3
)
2
-1-
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Worksheet by Kuta Software LLC
Identify the vertex and axis of symmetry of each. Then sketch the graph.
15) f (x) =
−3
(
x − 2
)
2
− 4
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
16) f (x) =
−
1
4
(
x − 1
)
2
+ 4
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
17) f (x) =
1
4
(
x + 4
)
2
+ 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
18) f (x) =
1
4
(
x + 5
)
2
+ 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
19) f (x) =
−2
(
x + 5
)
2
− 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
20) f (x) =
(
x + 2
)
2
− 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
-2-
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2 Name___________________________________
Period____Date________________
Vertex Form of Parabolas
Use the information provided to write the vertex form equation of each parabola.
1)
y =
x
2
+ 16
x + 71
y =
(
x + 8
)
2
+ 7
2)
y =
x
2
− 2
x − 5
y =
(
x − 1
)
2
− 6
3)
y =
−
x
2
− 14
x − 59
y =
−
(
x + 7
)
2
− 10
4)
y =
2
x
2
+ 36
x + 170
y =
2
(
x + 9
)
2
+ 8
5)
y =
x
2
− 12
x + 46
y =
(
x − 6
)
2
+ 10
6)
y =
x
2
+ 4
x
y =
(
x + 2
)
2
− 4
7)
y =
x
2
− 6
x + 5
y =
(
x − 3
)
2
− 4
8)
y =
(
x + 5
)(
x + 4
)
y =
(
x +
9
2
)
2
−
1
4
9)
1
2
(
y + 4
)
=
(
x − 7
)
2
y =
2
(
x − 7
)
2
− 4
10)
6
x
2
+ 12
x +
y + 13 = 0
y =
−6
(
x + 1
)
2
− 7
11)
162
x + 731 =
−
y − 9
x
2
y =
−9
(
x + 9
)
2
− 2
12)
x
2
− 12
x +
y + 40 = 0
y =
−
(
x − 6
)
2
− 4
13)
y =
x
2
+ 10
x + 33
y =
(
x + 5
)
2
+ 8
14)
y + 6 =
(
x + 3
)
2
y =
(
x + 3
)
2
− 6
-1-
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Worksheet by Kuta Software LLC
Identify the vertex and axis of symmetry of each. Then sketch the graph.
15) f (x) =
−3
(
x − 2
)
2
− 4
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertex:
(
2, −4
)
Axis of Sym.:
x = 2
16) f (x) =
−
1
4
(
x − 1
)
2
+ 4
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertex:
(
1, 4
)
Axis of Sym.:
x = 1
17) f (x) =
1
4
(
x + 4
)
2
+ 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertex:
(
−4, 3
)
Axis of Sym.:
x = −4
18) f (x) =
1
4
(
x + 5
)
2
+ 2
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertex:
(
−5, 2
)
Axis of Sym.:
x = −5
19) f (x) =
−2
(
x + 5
)
2
− 3
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertex:
(
−5, −3
)
Axis of Sym.:
x = −5
20) f (x) =
(
x + 2
)
2
− 1
x
y
−8 −6 −4 −2 2 4 6 8
−8
−6
−4
−2
2
4
6
8
Vertex:
(
−2, −1
)
Axis of Sym.:
x = −2
-2-
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