Name————————————————————————

Date —————————————

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

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. y B. y C. y
2

4 x
1 1

1 x 1 x

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

y y y

1 x
1 1

1 x 1 x

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

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y y y
Lesson 1.2

1 x
21
1 1

1 x 1 x

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)

y y y
1 1 1

1 x 1 x 21 x

Algebra 2
1-22 Chapter Resource Book
 Name———————————————————————— Date —————————————

Lesson
Practice A  continued
1.2 For use with the lesson “Graph Quadratic Functions in Vertex or Intercept Form”

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)

y y y
1

1 x

1 x
3

3 x

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)

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.

In Exercises 28 and 29, use the following information.

Golf  The flight of a particular golf shot can be modeled by the function

Lesson 1.2
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.

y
35
30
Height (yards)

25
20
15
10
5
0
0 80 160 240 x
Horizantal distance (yards)

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?

Algebra 2
Chapter Resource Book 1-23
 Lesson 1.1 Graph Quadratic
1 73
c. 24x 2 1 5 0; ​ 2}
​ 4 ​, } 1 
​ 8  ​  ​ 2
Functions in Standard Form, 7. Model A is preferable because profits are
continued positive and increasing.
Real-Life Application
Lesson 1.2 Graph Quadratic

answers
1. down 2. maximum value
Functions in Vertex or Intercept
3. y Form
Height (yards)

16
12 Teaching Guide
8
4 1.
0
0 4 8 12 16 20 24 28 32 36 40 x
Length (yards)

4. 15 yd
5. y
The graph of y 5 3x2 1 5 is a vertical shift of the
Height (yards)

16
12
8
graph of y 5 3x2.
4
2.
0
0 4 8 12 16 20 24 28 32 x
Length (yards)

6. about 19 yd 7. no

Challenge Practice
The graph of y 5 3(x 2 1)2 is a horizontal shift of
1. y
2. y
the graph of y 5 3x2. 3. The graph of y 5 x2 is
2
shifted k units vertically. 4. The graph of y 5 x2
2 x
is shifted h units horizontally.
Investigating Algebra Activity
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.

2
1. The parent function y 5 x 2 is shifted to the
2 x
right if a number is subtracted from x and to the
left if a number is added to x before squaring.
​1 2}   ​  ​; 2​ } ​  ​1 2} ​ 4  ​ 2​; 2​ }2 ​
3 61 3
36 2
35 425 35
​ 18 ​, 2​ } 18
​ 2 ​, } 2. The parent function y 5 x 2 is shifted down if
a number is subtracted from x 2 and up if a number
3. y
4. y
is added to x 2 after squaring. 3. The parent
2 function y 5 x 2 would be shifted 4 units to the
right and 5 units up. 4. The vertex form of a
21 x quadratic function makes it easy to see how the
2
x
parent function y 5 x 2 has been translated. The
2 value of h gives the horizontal shift and the value
of k gives the vertical shift.
​1 } 20 2 5 1​ }
13
​ 24  ​ 2​; }
6 6 15 377 15
​ 5 ​, 2​ } ​  ​; }
​   ​ ​ 2  ​, } ​ 2  ​ Practice Level A
5. The coefficient of the x 2-term of the quadratic 1. A 2. C 3. B
function is half of the coefficient of the x-term of 4. y
5. y

the linear equation. The coefficient of the x-term

of the quadratic function is the same as the
(3, 2)
constant term of the linear equation. 1
(1, 1)
1

2 50
1  2
2 x 1 x
6. a. 6x 2 4 5 0; ​ }
​ 3 ​, }
​ 3  ​  ​ x51 x53

1 51
b. 220x 1 5 5 0; ​ ​ } ​, 2​ }  ​  ​
4 8 1  2
Algebra 2
Chapter Resource Book A3
 Lesson 1.2 Graph Quadratic 4. y
5. y

Functions in Vertex or Intercept 1

Form, continued (21, 3) 1 x
(2, 21)
6. y
7. x 5 21 y 1
(21, 2)
x 5 21 1 x x52
1 1

1 x 1 x 6. y
7. x 5 21 y
2 x
22
(21, 22) 1 (21, 24)
x 5 21
1 x
x 5 22
8. y
9. y x53
1 x
21 (22, 23)
1
(3, 23)
1 x 8. y
9. y x54
(2, 21) (4, 8)
1 x
x52
x 5 22
23 2
10. y
1
11. 1
y
(22, 24) 2 x
(1, 0) (5, 0) (2, 0)
2 x 1 x

(22, 0) 10. y
11. y

2
(3, 24) (0, 24) (22, 0) (4, 0)
1
x53 x50
2 x (23, 0)
1 x

12. y
13. (21, 4) y x51 (2 5
2
,
1
)
2 4 (22, 0)
1 5
(26, 0) x 5 21 x 5 22
x
(1, 29)
21

(22, 0)
1
(1, 0) 12. y
13. y x51
2 x (1, 4)

Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.

(24, 24) 1
x 5 24 (23, 0)
(24, 0) 21 x
1
(23, 21) (22, 0) (21, 0)
14. y
1
15. y
22 (3, 0) x
(21, 0)
1
(2, 0)
x
x522
3
(2 , ) 3
2
75
4
x 5 23

1 14. y
x 52
5 15. y
(2 7 147
, 4 )
x 52 (27, 0) 2
3
(24, 0) (1, 0)
( 1
2
,
9
22 ) 3 x
2
(4, 0)
22 x 7
x 5 22
2 2 (1, 0)
16. y 5 2x 2 4x 1 3 17. y 5 2x 2 6x 2 4 6
(0, 0)
18. y 5 3x 2 2 12x 1 5 19. y 5 x 2 2 4x 1 3 ( 5
2
, 2 )
27
4 3 x

20. y 5 2x 2 1 10x 1 8 16. y 5 x 2 2 4x 1 10 17. y 5 22x 2 2 4x 1 1

21. y 5 23x 2 2 3x 1 18 18. y 5 3x 2 2 18x 1 15 19. y 5 x 2 2 6x 1 8
22. minimum, 1 23. maximum, 5 20. y 5 4x 2 1 12x 1 8
24. minimum, 27 25. minimum, 21 21. y 5 23x 2 1 3x 1 18
26. minimum, 28 27. maximum, 25 22. minimum, 3 23. maximum, 24
28. 280 29. 29.4 24. minimum, 23 25. minimum, 24
Practice Level B 25
26. minimum, 22 27. maximum, }
​ 4  ​
1. C 2. B 3. A
28. As a increases, the graph becomes more
narrow and the vertex moves down.
29. 260 30. 16.9

Algebra 2
A4 Chapter Resource Book