Name ———————————————————————
Date ————————————
Practice A
LESSON
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.
B.
C.
y
y
y
2
4
1
x
1
1
1
x
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
y
6. y 5 (x 1 1) 2 2 2
y
y
1
1
1
x
7. y 5 2(x 1 1) 2 1 2
1
x
8. y 5 4(x 2 2) 2 2 1
y
LESSON 1.2
x
1
9. y 5 22(x 2 3) 2 2 3
y
y
1
x
21
1
1
1
1
x
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)
y
y
1
y
1
1
1-22
12. y 5 (x 1 6)(x 1 2)
Algebra 2
Chapter Resource Book
x
1
1
x
21
x
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
1
Name ———————————————————————
LESSON
1.2
Date ————————————
Practice A
continued
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)
y
15. y 5 23(x 2 1)(x 1 4)
y
y
1
1
x
1
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)
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.
Height (yards)
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.
LESSON 1.2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
Find the minimum value or the maximum value of the function.
y
35
30
25
20
15
10
5
0
x
0
80
160 240
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
1
1 73
c. 24x 2 1 5 0; 2}, }
4 8
Lesson 1.1 Graph Quadratic
Functions in Standard Form,
continued
7. Model A is preferable because profits are
positive and increasing.
Lesson 1.2 Graph Quadratic
Functions in Vertex or Intercept
Form
Height (yards)
1. down 2. maximum value
y
16
12
8
4
0
Teaching Guide
ANSWERS
Real-Life Application
3.
2
1.
0 4 8 12 16 20 24 28 32 36 40 x
Length (yards)
5.
Height (yards)
4. 15 yd
y
16
12
8
4
0
The graph of y 5 3x2 1 5 is a vertical shift of the
graph of y 5 3x2.
2.
0 4 8 12 16 20 24 28 32 x
Length (yards)
6. about 19 yd 7. no
Challenge Practice
1.
2.
y
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.
y
2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
2
x
Investigating Algebra Activity
2
2
3
61
; 2}2
1 2}23, }
42
35
425
35
, 2}
; 2}
1 2}
18
36 2
18
3.
1. The parent function y 5 x 2 is shifted to the
x
4.
y
y
2
21
x
2
x
2
13 6
;}
1 }65, 2}
20 2 5
15 377 15
,} ;}
1}
2 24 2 2
2
5. The coefficient of the x -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.
1
1
2
2 50
6. a. 6x 2 4 5 0; }, }
3 3
51
1
b. 220x 1 5 5 0; }, 2}
8
4
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 x 2 is shifted down if
a number is subtracted from x 2 and up if a number
is added to x 2 after squaring. 3. The parent
function y 5 x 2 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 x 2 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.
5.
y
1
2
(3, 2)
1
(1, 1)
x51
y
x
1
x
x53
2
Algebra 2
Chapter Resource Book
A3
Lesson 1.2 Graph Quadratic
Functions in Vertex or Intercept
Form, continued
6.
7.
y
4.
1
1
x
(2, 21)
1
1
x 5 21
1
y
(21, 3)
y
x 5 21
(21, 2)
5.
y
x52
x
1
1
1
x
x
6.
7.
y
y
x 5 21
2
x
22
(21, 22)
(21, 24)
1
x 5 21
1 x
8.
9.
y
x 5 22
x53
y
1
x
21
1
(3, 23)
1
x
(22, 23)
8.
9.
y
(2, 21)
x52
1
x
x 5 22
2
23
11.
y
1
y
1
(1, 0) (5, 0)
2
(22, 24)
(2, 0)
1
x
10.
12.
1
(26, 0)
2
13.
(21, 4)
1
x 5 22
12.
y
13.
y
x51
(1, 4)
1
(23, 0)
15.
y
1
(2, 0)
1
x
21
(24, 0)
(23, 21) (22, 0)
y
3
75
4
( , )
3
2
x 2
14.
(
1
,
2
9
22
)
(4, 0)
y
2
1
(3, 0) x
2
16. y 5 2x 2 4x 1 3 17. y 5 2x 2 6x 2 4
18. y 5 3x 2 2 12x 1 5 19. y 5 x 2 2 4x 1 3
y
(7, 0)
( , )
7
2
147
4
(4, 0)
x
22
2
15.
5
x 52
(1, 0)
3
(21, 0)
x 5 23
1
3
x
22
x 52
7
x
(1, 0)
x 2
6
(
5
,
2
2
)
27
4
(0, 0)
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
A4
1 x
)
1
2 4 (22, 0)
x
(24, 24)
x 5 24
(21, 0)
5
,
2
5
(1, 0)
2
14.
(2
(1, 29)
x
(22, 0)
1
(23, 0)
x
x51
y
x 5 21
21
y
(4, 0)
2
x50
y
11.
y
(22, 0)
(0, 24)
x53
x
x
(22, 0)
(3, 24)
2
Algebra 2
Chapter Resource Book
28. As a increases, the graph becomes more
narrow and the vertex moves down.
29. 260 30. 16.9
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10.
x54
(4, 8)
y