Lesson Practice A 1.2 For use with the lesson “Graph...

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Match the equation with its graph.

1. y 5 (x 2 1)2 2. y 5 (x 2 2)(x 1 4) 3. y 5 22(x 1 1)2 1 3

A.

x

y

1

1

B.

x

y

1

1

C.

x

y2

4

Graph the function. Label the vertex and axis of symmetry.

4. y 5 (x 2 1)2 1 1 5. y 5 (x 2 3)2 1 2 6. y 5 (x 1 1)2 2 2

x

y

1

1

x

y

1

1

x

y

1

1

7. y 5 2(x 1 1)2 1 2 8. y 5 4(x 2 2)2 2 1 9. y 5 22(x 2 3)2 2 3

x

y

1

1

x

y

1

1

x

y

211

Graph the function. Label the vertex, axis of symmetry, and x-intercepts.

10. y 5 (x 2 1)(x 2 5) 11. y 5 (x 1 2)(x 2 2) 12. y 5 (x 1 6)(x 1 2)

x

y1

1

x

y1

1

x

y1

21

Practice AFor use with the lesson “Graph Quadratic Functions in Vertex or Intercept Form”

Algebra 2Chapter Resource Book1-22

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1.2

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13. y 5 2(x 1 3)(x 2 1) 14. y 5 2(x 1 1)(x 2 2) 15. y 5 23(x 2 1)(x 1 4)

x

y

1

1

x

y1

1

x

y

3

3

Write the quadratic function in standard form.

16. y 5 2(x 2 1)2 1 1 17. y 5 2(x 1 3)2 1 5

18. y 5 3(x 2 2)2 2 7 19. y 5 (x 2 3)(x 2 1)

20. y 5 2(x 1 1)(x 1 4) 21. y 5 23(x 2 2)(x 1 3)

Find the minimum value or the maximum value of the function.

22. y 5 (x 2 3)2 1 1 23. y 5 22(x 1 1)2 1 5

24. y 5 4(x 2 2)2 2 7 25. y 5 (x 1 3)(x 1 1)

26. y 5 2(x 2 1)(x 2 5) 27. y 5 24(x 2 3)(x 1 2)

In Exercises 28 and 29, use the following information.

Golf The flight of a particular golf shot can be modeled by the function y 5 20.0015x(x 2 280) where x is the horizontal distance (in yards) from the impact point and y is the height (in yards). The graph is shown below.

0 80 160 240 x05

101520253035

y

Horizantal distance (yards)

Hei

gh

t (y

ard

s)

28. How many yards away from the impact point does the golf ball land?

29. What is the maximum height in yards of the golf shot?

Practice A continuedFor use with the lesson “Graph Quadratic Functions in Vertex or Intercept Form”

Algebra 2Chapter Resource Book 1-23

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on

1.2

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Lesson Graph Quadratic Functions in Standard Form, continuedReal-Life Application

1. down 2. maximum value

3.

x

y

0048

1216

4 8 12 16 20 24 28 32 36 40Length (yards)

Hei

gh

t (y

ard

s)

4. 15 yd

5.

x

y

0048

1216

4 8 12 16 20 24 28 32Length (yards)

Hei

gh

t (y

ard

s)

6. about 19 yd 7. no

Challenge Practice

1.

x

y

2

2

2.

x

y

2

2

1 2 35

} 18

, 2 425

} 36

2 ; 2 35

} 18

1 2 3 } 2 ,

61 }

4 2 ; 2

3 } 2

3.

x

y

2

21

4.

x

y

2

2

1 6 } 5 , 2 13

} 20 2 ; 6 } 5 1 15 }

2 ,

377 }

24 2 ; 15

} 2

5. The coefficient of the x2-term of the quadratic function is half of the coefficient of the x-term of the linear equation. The coefficient of the x-term of the quadratic function is the same as the constant term of the linear equation.

6. a. 6x 2 4 5 0; 1 2 } 3 ,

50 }

3 2

b. 220x 1 5 5 0; 1 1 } 4 , 2

51 } 8 2

c. 24x 2 1 5 0; 1 2 1 } 4 ,

73 }

8 2

7. Model A is preferable because profits are positive and increasing.

Lesson Graph Quadratic Functions in Vertex or Intercept FormTeaching Guide

1.

The graph of y 5 3x2 1 5 is a vertical shift of the graph of y 5 3x2.

2.

The graph of y 5 3(x 2 1)2 is a horizontal shift of the graph of y 5 3x2. 3. The graph of y 5 x2 is shifted k units vertically. 4. The graph of y 5 x2 is shifted h units horizontally.

Investigating Algebra Activity

1. The parent function y 5 x2 is shifted to the right if a number is subtracted from x and to the left if a number is added to x before squaring.

2. The parent function y 5 x2 is shifted down if a number is subtracted from x2 and up if a number is added to x2 after squaring. 3. The parent function y 5 x2 would be shifted 4 units to the right and 5 units up. 4. The vertex form of a quadratic function makes it easy to see how the parent function y 5 x2 has been translated. The value of h gives the horizontal shift and the value of k gives the vertical shift.

Practice Level A

1. A 2. C 3. B

4.

x

y

1

2

(1, 1)

x 5 1

5.

x

y

1

1

(3, 2)

x 5 3

an

sw

er

s

Algebra 2Chapter Resource Book A3

1.1

1.2

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Lesson Graph Quadratic Functions in Vertex or Intercept Form, continued 6.

x

y

1

1

(21, 22)x 5 21

7.

x

y

1

1

(21, 2)x 5 21

8.

x

y

1

1

(2, 21)x 5 2

9. x

y

211

x 5 3

(3, 23)

10.

x

y1

2

x 5 3(3, 24)

(1, 0) (5, 0) 11.

x

y1

1

x 5 0(0, 24)

(22, 0)

(2, 0)

12.

x

y1

21

x 5 24(24, 24)

(22, 0)

(26, 0) 13.

x

y

1

2

(21, 4)

(23, 0)

x 5 21

(1, 0)

14.

x

y1

1

(21, 0)

x 5

(2, 0)

12

( )12

92, 2

15.

x

y

3

3

x 5 232

(24, 0) (1, 0)

( )32

754 2 ,

16. y 5 2x2 2 4x 1 3 17. y 5 2x2 2 6x 2 4

18. y 5 3x2 2 12x 1 5 19. y 5 x2 2 4x 1 3

20. y 5 2x2 1 10x 1 8

21. y 5 23x2 2 3x 1 18

22. minimum, 1 23. maximum, 5

24. minimum, 27 25. minimum, 21


28. 280 29. 29.4

Practice Level B

1. C 2. B 3. A

4.

x

y

1

1x 5 21

(21, 3)

5.

x

y

1

1

x 5 2

(2, 21)

6.

x

y

1

1

x 5 22

(22, 23)

7. x

y

222

(21, 24)

x 5 21

8.

x

y

23

1

(22, 24)

x 5 22

9.

x

y

2

2

(4, 8)x 5 4

10.

x

y

2

2

(1, 29)

(4, 0)(22, 0)

x 5 1

11.

x

y

1

1

(23, 0)

(22, 0)

x 5 252

( )52

142 , 2

12.

x

y

1

21

(23, 21)(24, 0)

(22, 0)

x 5 23

13.

x

y

1

22

(1, 4)

(3, 0)(21, 0)

x 5 1

14.

x

y

2

22

(1, 0)

x 5

(4, 0)

52

( )52

274, 2

15.

x

y

6

3

x 5 272

(0, 0)

( )72

14742 ,

(27, 0)

16. y 5 x2 2 4x 1 10 17. y 5 22x2 2 4x 1 1

18. y 5 3x2 2 18x 1 15 19. y 5 x2 2 6x 1 8

20. y 5 4x2 1 12x 1 8

21. y 5 23x2 1 3x 1 18


24. minimum, 23 25. minimum, 24


} 4

28. As a increases, the graph becomes more narrow and the vertex moves down.

29. 260 30. 16.9

Algebra 2Chapter Resource BookA4

1.2

Lesson Practice A 1.2 For use with the lesson “Graph...

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