Properties of Parabolas - Kuta Software LLC

Kuta Software - Infinite Algebra 2 Name___________________________________
Date________________ Period____
Properties of Parabolas
2) y = 2x2 − 4x − 2
Identify the vertex of each.
1) y = x2 + 16x + 64

3) y = −x2 + 18x − 75 4) y = −3x2 + 12x − 10

Graph each equation. 6) y = −x2 − 6x − 10
5) y = x2 − 2x − 3
y
y 8
8
6
6
4
4
2
2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

Identify the min/max value of each. Then sketch the graph.

7) f (x) = −x2 + 8x − 20 8) f (x) = − 1 x2 + 4 16
x−
y 3 33
8
y
6 8

46

24

−8 −6 −4 −2 2 4 6 8x 2
−2
−8 −6 −4 −2 2 4 6 8x
−4 −2

−6 −4

−8 −6

−8

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9) f (x) = x2 + 2x − 1 10) f (x) = −x2 − 10x − 30

y y
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

Identify the vertex, axis of symmetry, and min/max value of each.

11) f (x) = 3x2 − 54x + 241 12) f (x) = x2 − 18x + 86

13) f (x) = − 4 x2 + 48 114 14) f (x) = −2x2 − 20x − 46
x−
555

15) f (x) = − 1 x2 + 7 16) f (x) = x2 − 12x + 44
4 18) f (x) = x2 + 4x + 5

17) f (x) = 1 x2 − x + 9
4

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Kuta Software - Infinite Algebra 2 Name___________________________________
Date________________ Period____
Properties of Parabolas
2) y = 2x2 − 4x − 2
Identify the vertex of each.
1) y = x2 + 16x + 64 (1, −4)

(−8, 0)

3) y = −x2 + 18x − 75 4) y = −3x2 + 12x − 10

(9, 6) (2, 2)

Graph each equation. 6) y = −x2 − 6x − 10
5) y = x2 − 2x − 3
y
y 8
8
6
6
4
4
2
2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

Identify the min/max value of each. Then sketch the graph.

7) f (x) = −x2 + 8x − 20 8) f (x) = − 1 x2 + 4 16
x−
y 3 33
8 Max value = −4

6 y Max value = −4
8

46

24

−8 −6 −4 −2 2 4 6 8x 2
−2
−8 −6 −4 −2 2 4 6 8x
−4 −2

−6 −4

−8 −6

−8

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9) f (x) = x2 + 2x − 1 Min value = −2 10) f (x) = −x2 − 10x − 30 Max value = −5

y y
8 8

6 6

4 4

2 2

−8 −6 −4 −2 2 4 6 8x −8 −6 −4 −2 2 4 6 8x
−2 −2
−4 −4
−6 −6
−8 −8

Identify the vertex, axis of symmetry, and min/max value of each.

11) f (x) = 3x2 − 54x + 241 12) f (x) = x2 − 18x + 86

Vertex: (9, −2) Vertex: (9, 5)

Axis of Sym.: x = 9 Axis of Sym.: x = 9
Min value = −2 Min value = 5

13) f (x) = − 4 x2 + 48 114 14) f (x) = −2x2 − 20x − 46
x−
555 Vertex: (−5, 4)

Vertex: (6, 6) Axis of Sym.: x = −5
Max value = 4
Axis of Sym.: x = 6
Max value = 6

15) f (x) = − 1 x2 + 7 16) f (x) = x2 − 12x + 44
4
Vertex: (6, 8)
Vertex: (0, 7)
Axis of Sym.: x = 6
Axis of Sym.: x = 0 Min value = 8
Max value = 7

17) f (x) = 1 x2 − x + 9 18) f (x) = x2 + 4x + 5
4
Vertex: (−2, 1)
Vertex: (2, 8)
Axis of Sym.: x = −2
Axis of Sym.: x = 2 Min value = 1
Min value = 8

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