Write each function in vertex form.

[Pages:12]3-5 Transformations of Quadratic Graphs

Write each function in vertex form. 1.

SOLUTION:

4. MULTIPLE CHOICE Which function is shown in the graph?

2. SOLUTION:

A y = ?(x + 3)2 + 6 B y = ?(x ? 3)2 ? 6 C y = ?2(x + 3)2 + 6 D y = ?2(x ? 3)2 ? 6

SOLUTION:

From the figure, the vertex (h, k) of the parabola is (?3, 6). Substitute (?5, 2) for (x, y) in the vertex form to find a.

3. SOLUTION:

4. MULTIPLE CHOICE Which function is shown in the graph?

The graph represents the function The answer is choice A.

Graph each function. 5.

SOLUTION: The vertex is at (3, ?4) and the axis of symmetry is x = 3. Since a = 1 > 0, the graph opens up.

A y = ?(x + 3)2 + 6 B y = ?(x ? 3)2 ? 6 C y = ?2(x + 3)2 + 6 D y = ?2(x ? 3)2 ? 6

SOLUTION:

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From the figure, the vertex (h, k) of the parabola is (?3, 6). Substitute (?5, 2) for (x, y) in the vertex form to find a.

6. SOLUTION:

The vertex is at (0, 5) and the axis of symmetry is x = 0. Since a = ?2 < 0, the graph opens down.

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3-5 Transformations of Quadratic Graphs

6. SOLUTION:

9. SOLUTION:

The vertex is at (0, 5) and the axis of symmetry is x = 0. Since a = ?2 < 0, the graph opens down.

10. SOLUTION:

7.

SOLUTION: The vertex is at (?6, ?8) and the axis of symmetry s

x = ?6. Since

the graph opens up.

11. SOLUTION:

Write each function in vertex form. 8.

SOLUTION:

12. SOLUTION:

9. eSolutSioOnsLMUanTuIaOl -NPo: wered by Cognero

13. SOLUTION:

14. SOLUTION:

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3-5 Transformations of Quadratic Graphs 13.

SOLUTION:

14. SOLUTION:

15. SOLUTION:

SOLUTION:

17. SOLUTION:

18. SOLUTION:

19. SOLUTION:

16. SOLUTION:

17. SOLUTION:

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20. FIREWORKS During an Independence Day fireworks show, the height h in meters of a specific rocket after t seconds can be modeled by h = ?4.9(t ? 4)2 + 80. Graph the function. SOLUTION: Assign the height h in y-axis and the time t in x-axis. The vertex of the graph is at (4, 80) and the axis of symmetry is t = 4. Since a = ?4.9 < 0, the graph opens down.

21. FINANCIAL LITERACY A bicycle rental shPoapge 3 rents an average of 120 bicycles per week and charges $25 per day. The manager estimates that

3-5 Transformations of Quadratic Graphs

21. FINANCIAL LITERACY A bicycle rental shop rents an average of 120 bicycles per week and charges $25 per day. The manager estimates that there will be 15 additional bicycles rented for each $1 reduction in the rental price. The maximum income the manager can expect can be modeled by y = ? 15x2 + 255x + 3000, where y is the weekly income and x is the number of bicycles rented. Write this function in vertex form. Then graph.

SOLUTION:

Graph each function. 22.

SOLUTION: The vertex is at (5, 3) and the axis of symmetry is x = 5. Since a = 1 > 0, the graph opens up.

23. SOLUTION:

The vertex of the graph is at (8.5, 4083.75) and the axis of symmetry is x = 8.5. a = ?15 < 0. Therefore, the graph opens down.

The vertex is at (0, ?8) and the axis of symmetry is x = 0. a = 9 > 0, Therefore, the graph opens up.

Graph each function. 22.

SOLUTION: The vertex is at (5, 3) and the axis of symmetry is x = 5. Since a = 1 > 0, the graph opens up.

24.

SOLUTION: The vertex is at (5, 0) and the axis of symmetry is x = 5. Since a = ?2 < 0, the graph opens down.

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23.

SOLUTION:

25.

SOLUTION: The vertex is at (?6, 6) and the axis of symmetry is

.

Therefore, the graph opensPaugpe.4

3-5 Transformations of Quadratic Graphs

25.

SOLUTION: The vertex is at (?6, 6) and the axis of symmetry is

.

Therefore, the graph opens up.

28.

SOLUTION:

The vertex is at (0, 10) and the axis of symmetry is

x = 0. Since

the graph opens up.

26.

SOLUTION:

The vertex is at (5, ?2) and the axis of symmetry is

x = 5.

Therefore, the graph opens down.

29.

SOLUTION:

The vertex is at (?3, 0) and the axis of symmetry is

.

Therefore, the graph opens

down.

27.

SOLUTION: The vertex is at (0, ?5) and the axis of symmetry is x

= 0.

Therefore, the graph opens down.

30.

SOLUTION: The vertex is at (3, ?10) and the axis of symmetry is

.

Therefore, the graph opens up.

28.

SOLUTION:

The vertex is at (0, 10) and the axis of symmetry is

x = 0. Since

the graph opens up.

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31. SOLUTION: The vertex is at (9, ?7) and the axis of symmetry is x = 9. Since a = 1 > 0, the graph opens up.

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3-5 Transformations of Quadratic Graphs

31. SOLUTION: The vertex is at (9, ?7) and the axis of symmetry is x = 9. Since a = 1 > 0, the graph opens up.

32.

SOLUTION: The vertex is at (0, ?8) and the axis of symmetry is x

= 0.

Therefore, the graph opens down.

34. CCSS MODELING A sailboard manufacturer uses an automated process to manufacture the masts for

its sailboards. The function

is

programmed into a computer to make one such mast. a. Write the quadratic function in vertex form. Then graph the function. b. Describe how the manufacturer can adjust the function to make its masts with a greater or smaller curve.

SOLUTION: a.

The vertex of the function is

33.

SOLUTION:

The vertex is at (10, ?10) and the axis of symmetry

is

.

Therefore, the graph opens

down.

b. They can adjust the coefficient of x2.

Write an equation in vertex form for each parabola.

34. CCSS MODELING A sailboard manufacturer uses an automated process to manufacture the masts for

its sailboards. The function

is

programmed into a computer to make one such mast. a. Write the quadratic function in vertex form. Then eSolutgiornaspMhatnhuealfu- Pnocwtieorned. by Cognero b. Describe how the manufacturer can adjust the function to make its masts with a greater or smaller

35.

SOLUTION:

From the figure, the vertex (h, k) of the parabola is

(6, 1). Substitute (7, 10) for (x, y) in the vertex form

to find a.

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3-5 Tbr.aTnhsefoyrcmanataidojnusstotfhQe ucoaedfrfaictiiecnGt orfapx2h.s

The graph represents the equation

.

Write an equation in vertex form for each parabola.

35.

SOLUTION: From the figure, the vertex (h, k) of the parabola is (6, 1). Substitute (7, 10) for (x, y) in the vertex form to find a.

37.

SOLUTION: From the figure, the vertex (h, k) of the parabola is (3, 0). Substitute (6, ?6) for (x, y) in the vertex form to find a.

The graph represents the equation

The graph represents the equation

36.

SOLUTION: From the figure, the vertex (h, k) of the parabola is (?4, 3). Substitute (?3, 6) for (x, y) in the vertex form to find a.

38.

SOLUTION: From the figure, the vertex (h, k) of the parabola is (5, 4). Substitute (6, 1) for (x, y) in the vertex form to find a.

The graph represents the equation

.

The graph represents the equation

eS3o7l.utions Manual - Powered by Cognero SOLUTION: From the figure, the vertex (h, k) of the parabola is

39.

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SOLUTION: From the figure, the vertex (h, k) of the parabola is

3-5 TTrhaengsfroaprmh raetpiorensseonftsQthueaedqruaatitcioGn raphs

The function of the parabola is

Write each function in vertex form. Then identify the vertex, axis of symmetry, and direction of opening. 41.

SOLUTION:

39.

SOLUTION: From the figure, the vertex (h, k) of the parabola is (0, 5). Substitute (3, 8) for (x, y) in the vertex form to find a.

The function of the parabola is

40. SOLUTION: From the figure, the vertex (h, k) of the parabola is (?3, 2). Substitute (?1, 8) for (x, y) in the vertex form to find a.

Vertex:

Axis of symmetry: Since a = 3 > 0, the graph opens up.

42. SOLUTION:

The function of the parabola is

Write each function in vertex form. Then identify the vertex, axis of symmetry, and direction of opening. 41.

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Vertex:

Axis of symmetry: Since a = ?2 < 0, the graph opens down. 43. SOLUTION:

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