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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
Les
so
n 1
.2
Lesson
1.2
Name ——————————————————————— Date ————————————Co
pyrig
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Hou
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Har
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ompa
ny. A
ll rig
hts
rese
rved
.
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
Less
on
1.2
Lesson
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
26. minimum, 28 27. maximum, 25
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
22. minimum, 3 23. maximum, 24
24. minimum, 23 25. minimum, 24
26. minimum, 22 27. maximum, 25
} 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