Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Algebra 2 - Unit 2 Test
1. Factor 15x3
− 6x2
− 25x + 10 by grouping.
2. Factor the trinomial a2
+ 14a + 48.
3. Factor 2x2
+ 7x + 6.
4. Factor the trinomial 42n2
− n − 30.
5. The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry through the focus,
with endpoints on the parabola. Find the length of the latus rectum of the parabola y =1
12x
2.
____ 6. Identify the axis of symmetry for the graph of f(x) = x2
+ 2x − 3.
F. x = −1 H. y = −1
G. y = −4 J. x = −4
7. Find the zeros of the function h x( ) = x2
+ 23x + 60 by factoring.
8. A quadratic equation has the following coefficients: a = 2, b = –2, and c = 1. Write the solution(s) of the equation.
9. Solve the equation 2x2
+ 18 = 0.
Name: ________________________ ID: A
2
10. Write a quadratic function in standard form with zeros 6 and –8.
11. Solve the equation x2
= 3 − 2x by completing the square.
12. Write the equation in standard form for the parabola with vertex (0,0) and directrix y = −7.
13. Solve x2
= −4 using square roots.
____ 14. Solve 3x2 – 6x + 1 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.
F. There are no solutions. H. x ≈ 6.82 or x ≈ 5.18
G. x ≈ 10.90 or x ≈ 1.10 J. x ≈ 1.82 or x ≈ 0.18
____ 15. Find the discriminant of −3x2
− 4x + 6 = 0.
A. 72 C. 89
B. 88 D. 90
16. Write a quadratic function that fits the points (0, 6), (2, 4), and (3, 6).
Name: ________________________ ID: A
3
17. For the equation x2
− 6x − 8y − 23 = 0 find the coordinates of the vertex and focus, and the equations of the
directrix and the axis of symmetry. Then graph the equation.
____ 18. Write the equation of the parabola y = x2
− 4x − 29 in standard form.
F. y + 33 = x − 2( )2
H. y + 4 = x − 2( )2
G. y + 29 = x − 2( )2
J. y − 2 = x − 2( )2
19. Express 8 −84 in terms of i.
20. Find the values of x and y that make the equation −9x + 8i = −54 + (16y)i true.
21. Find the complex conjugate of 3i + 4.
22. Find the absolute value −7 − 9i| |.
23. Subtract. Write the result in the form a + bi.
(5 – 2i) – (6 + 8i)
Name: ________________________ ID: A
4
24. Multiply 6i 4 − 6i( ). Write the result in the form a + bi.
25. Simplify −8i20
.
26. Simplify −2 + 2i
5 + 3i.
27. Simplify the expression 50
98.
28. Simplify 7
5 by rationalizing the denominator.
29. Graph y ≤ −x2
− 5x + 4.
Name: ________________________ ID: A
5
30. Solve −8x + 4y = 48
y + 3 = (x + 6)2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
.
____ 31. Graph the system.
x2
+ y2
≤ 49
y ≤ 3 − x2
A. C.
B. D.
Name: ________________________ ID: A
6
32. The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds
x (miles per hour).
Speed, x
(mi/h)
50 55 60 65 70 75 80 85 90
Distance, y
(100 m)
20 25 35 50 70 95 125 160 200
Find an equation of the quadratic function that models the data, and predict the stopping distance for the train
traveling at 95 miles per hour.
33. What quadratic function does the graph represent?
ID: A
1
Algebra 2 - Unit 2 TestAnswer Section
1. ANS:
(5x − 2)(3x2
− 5)
DIF: Average
2. ANS: a + 6( ) a + 8( )
DIF: Basic
3. ANS: x + 2( ) 2x + 3( )
DIF: Basic
4. ANS: (6n + 5)(7n − 6)
DIF: Advanced
5. ANS: 12
DIF: Advanced
6. ANS: F DIF: Average
7. ANS: x = −20 or x = −3
DIF: Basic
8. ANS: 0.5, 0.5
9. ANS: x = ±3i
DIF: Average
10. ANS:
f(x) = x2
+ 2x − 48
DIF: Average
11. ANS: x = 1 or x = –3
DIF: Basic
12. ANS:
y =1
28x
2
DIF: Average
ID: A
2
13. ANS: There is no solution.
DIF: Basic
14. ANS: J DIF: Average
15. ANS: B
16. ANS:
f x( ) = x2
− 3x + 6
DIF: Average
17. ANS:
Vertex: 3, − 4ÊËÁÁ ˆ
¯˜̃ ; focus: 3, − 2Ê
ËÁÁ ˆ
¯˜̃; directrix:y = − 6; axis of symmetry:x = 3
18. ANS: F
19. ANS:
16i 21
DIF: Average
20. ANS:
x = 6, y =1
2
DIF: Average
21. ANS: 4 − 3i
DIF: Basic
22. ANS:
130
DIF: Basic
23. ANS: –1 – 10i
DIF: Average
ID: A
3
24. ANS: 36 + 24i
DIF: Basic
25. ANS: –8
DIF: Average
26. ANS:
−2
17 +
8
17i
DIF: Average
27. ANS: 5
7
DIF: Basic
28. ANS:
35
5
DIF: Average
29. ANS:
DIF: Average
30. ANS: (−7, − 2) and (−3, 6)
DIF: Average
31. ANS: D
ID: A
4
32. ANS:
y = 0.1x2
− 9.5x + 245
about 245 hundred meters
DIF: Advanced
33. ANS:
f(x) = −x2
+ 8x − 14
DIF: Advanced
ID: A Algebra 2 - Unit 2 Test [Answer Strip]
_____ 6.F
_____14.J
_____15.B
_____18.F
_____31.D
Name: ________________________ Class: ___________________ Date: __________ ID: B
1
Algebra 2 - Unit 2 Test
1. Factor 15x3
− 6x2
− 25x + 10 by grouping.
2. Factor the trinomial m2
+ 10m + 16.
3. Factor 2x2
+ 7x + 6.
4. Factor the trinomial 63x2
− 43x − 30.
5. The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry through the focus,
with endpoints on the parabola. Find the length of the latus rectum of the parabola y =1
24x
2.
____ 6. Identify the axis of symmetry for the graph of f(x) = −x2
+ 4x + 5.
F. x = 9 H. y = 2
G. y = 9 J. x = 2
7. Find the zeros of the function h x( ) = x2
+ 19x + 90 by factoring.
8. A quadratic equation has the following coefficients: a = –1, b = 3, and c = –3. Write the solution(s) of the equation.
9. Solve the equation 5x2
+ 45 = 0.
Name: ________________________ ID: B
2
10. Write a quadratic function in standard form with zeros 8 and –2.
11. Solve the equation x2
= 65 − 8x by completing the square.
12. Write the equation in standard form for the parabola with vertex (0,0) and directrix y = −4.
13. Solve x2
= −25 using square roots.
____ 14. Solve 3x2 – x – 1 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.
F. x ≈ 1.60 or x ≈ 0.40 H. x ≈ 0.77 or x ≈ –0.43
G. x ≈ 4.61 or x ≈ –2.61 J. There are no solutions.
____ 15. Find the discriminant of 2x2
+ 2x − 3 = 0.
A. 28 C. 29
B. 30 D. 24
16. Write a quadratic function that fits the points (0, 4), (3, 4), and (4, 8).
Name: ________________________ ID: B
3
17. For the equation x2
− 6x − 8y − 23 = 0 find the coordinates of the vertex and focus, and the equations of the
directrix and the axis of symmetry. Then graph the equation.
____ 18. Write the equation of the parabola y = x2
− 8x − 69 in standard form.
F. y + 16 = x − 4( )2
H. y + 69 = x − 4( )2
G. y + 85 = x − 4( )2
J. y − 4 = x − 4( )2
19. Express 7 −99 in terms of i.
20. Find the values of x and y that make the equation −2x + 9i = 8 + (45y)i true.
21. Find the complex conjugate of −7i − 17.
22. Find the absolute value −9 + 7i| |.
23. Add. Write the result in the form a + bi.
(–7 – i) + (6 + 5i)
Name: ________________________ ID: B
4
24. Multiply 5i 4 − 2i( ). Write the result in the form a + bi.
25. Simplify 9i16
.
26. Simplify 2 + 5i
3 − 2i.
27. Simplify the expression 147
192.
28. Simplify 14
3 by rationalizing the denominator.
29. Graph y ≤ −5x2
+ 2x − 4.
Name: ________________________ ID: B
5
30. Solve −8x + 4y = 20
y + 8 = (x + 5)2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
.
____ 31. Graph the system.
x2
+ y2
≤ 16
y ≤ 3 − x2
A. C.
B. D.
Name: ________________________ ID: B
6
32. The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds
x (miles per hour).
Speed, x
(mi/h)
60 65 70 75 80 85 90 95 100
Distance, y
(100 m)
35 50 70 95 125 160 200 245 295
Find an equation of the quadratic function that models the data, and predict the stopping distance for the train
traveling at 105 miles per hour.
33. What quadratic function does the graph represent?
ID: B
1
Algebra 2 - Unit 2 TestAnswer Section
1. ANS:
(5x − 2)(3x2
− 5)
DIF: Average
2. ANS: m + 8( ) m + 2( )
DIF: Basic
3. ANS: x + 2( ) 2x + 3( )
DIF: Basic
4. ANS: (7x + 3)(9x − 10)
DIF: Advanced
5. ANS: 24
DIF: Advanced
6. ANS: J DIF: Average
7. ANS: x = −10 or x = −9
DIF: Basic
8. ANS: 1.5, 1.5
9. ANS: x = ±3i
DIF: Average
10. ANS:
f(x) = x2
− 6x − 16
DIF: Average
11. ANS: x = 5 or x = –13
DIF: Basic
12. ANS:
y =1
16x
2
DIF: Average
ID: B
2
13. ANS: There is no solution.
DIF: Basic
14. ANS: H DIF: Average
15. ANS: A
16. ANS:
f x( ) = x2
− 3x + 4
DIF: Average
17. ANS:
Vertex: 3, − 4ÊËÁÁ ˆ
¯˜̃ ; focus: 3, − 2Ê
ËÁÁ ˆ
¯˜̃; directrix:y = − 6; axis of symmetry:x = 3
18. ANS: G
19. ANS:
21i 11
DIF: Average
20. ANS:
x = −4, y =1
5
DIF: Average
21. ANS: −17 + 7i
DIF: Basic
22. ANS:
130
DIF: Basic
23. ANS: –1 + 4i
DIF: Average
ID: B
3
24. ANS: 10 + 20i
DIF: Basic
25. ANS: 9
DIF: Average
26. ANS:
−4
13 +
19
13i
DIF: Average
27. ANS: 7
8
DIF: Basic
28. ANS:
42
3
DIF: Average
29. ANS:
DIF: Average
30. ANS: (−6, − 7) and (−2, 1)
DIF: Average
31. ANS: B
ID: B
4
32. ANS:
y = 0.1x2
− 9.5x + 245
about 350 hundred meters
DIF: Advanced
33. ANS:
f(x) = −x2
+ 10x − 21
DIF: Advanced
ID: B Algebra 2 - Unit 2 Test [Answer Strip]
_____ 6.J
_____14.H
_____15.A
_____18.G
_____31.B
Name: ________________________ Class: ___________________ Date: __________ ID: C
1
Algebra 2 - Unit 2 Test
1. Factor 15x3
− 6x2
− 25x + 10 by grouping.
2. Factor the trinomial m2
+ 10m + 16.
3. Factor 3x2
− 17x + 10.
4. Factor the trinomial 9y2
− 17y − 30.
5. The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry through the focus,
with endpoints on the parabola. Find the length of the latus rectum of the parabola y =1
16x
2.
____ 6. Identify the axis of symmetry for the graph of f(x) = 2x2
+ 4x + 2.
F. y = 0 H. x = −1
G. x = 0 J. y = −1
7. Find the zeros of the function h x( ) = x2
+ 15x + 50 by factoring.
8. A quadratic equation has the following coefficients: a = 1, b = 9, and c = 9. Write the solution(s) of the equation.
9. Solve the equation 7x2
+ 63 = 0.
Name: ________________________ ID: C
2
10. Write a quadratic function in standard form with zeros 6 and –4.
11. Solve the equation x2
= 39 − 10x by completing the square.
12. Write the equation in standard form for the parabola with vertex (0,0) and directrix y = −10.
13. Solve x2
= 16 using square roots.
____ 14. Solve 2x2 + 3x – 4 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.
F. x ≈ 0.85 or x ≈ –2.35 H. x ≈ 3.40 or x ≈ –9.40
G. x ≈ –1.40 or x ≈ –4.60 J. There are no solutions.
____ 15. Find the discriminant of −6x2
− 5x + 6 = 0.
A. 169 C. 171
B. 170 D. 144
16. Write a quadratic function that fits the points (0, 4), (2, 2), and (4, 8).
Name: ________________________ ID: C
3
17. For the equation x2
− 4x − 8y + 28 = 0 find the coordinates of the vertex and focus, and the equations of the
directrix and the axis of symmetry. Then graph the equation.
____ 18. Write the equation of the parabola y = x2
+ 10x − 55 in standard form.
F. y + 25 = x + 5( )2
H. y + 80 = x + 5( )2
G. y + 55 = x + 5( )2
J. y + 5 = x + 5( )2
19. Express 4 −54 in terms of i.
20. Find the values of x and y that make the equation −11x + 8i = 22 + (40y)i true.
21. Find the complex conjugate of −20i + 10.
22. Find the absolute value 3 + 9i| |.
23. Subtract. Write the result in the form a + bi.
(–8 – 5i) – (–2 – i)
Name: ________________________ ID: C
4
24. Multiply 3i 6 − 3i( ). Write the result in the form a + bi.
25. Simplify −9i20
.
26. Simplify −5 + 4i
2 + 5i.
27. Simplify the expression 108
147.
28. Simplify 5
7 by rationalizing the denominator.
29. Graph y ≥ 3x2
− x + 2.
Name: ________________________ ID: C
5
30. Solve −8x + 4y = 8
y + 5 = (x + 2)2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
.
____ 31. Graph the system.
x2
+ y2
≤ 4
y ≤ 6 − x2
A. C.
B. D.
Name: ________________________ ID: C
6
32. The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds
x (miles per hour).
Speed, x
(mi/h)
55 60 65 70 75 80 85 90 95
Distance, y
(100 m)
25 35 50 70 95 125 160 200 245
Find an equation of the quadratic function that models the data, and predict the stopping distance for the train
traveling at 100 miles per hour.
33. What quadratic function does the graph represent?
ID: C
1
Algebra 2 - Unit 2 TestAnswer Section
1. ANS:
(5x − 2)(3x2
− 5)
DIF: Average
2. ANS: m + 8( ) m + 2( )
DIF: Basic
3. ANS: x − 5( ) 3x − 2( )
DIF: Basic
4. ANS: (y − 3)(9y + 10)
DIF: Advanced
5. ANS: 16
DIF: Advanced
6. ANS: H DIF: Average
7. ANS: x = −10 or x = −5
DIF: Basic
8. ANS: –1.15, –7.85
9. ANS: x = ±3i
DIF: Average
10. ANS:
f(x) = x2
− 2x − 24
DIF: Average
11. ANS: x = 3 or x = –13
DIF: Basic
12. ANS:
y =1
40x
2
DIF: Average
ID: C
2
13. ANS: The solutions are 4 and –4.
DIF: Basic
14. ANS: F DIF: Average
15. ANS: A
16. ANS:
f x( ) = x2
− 3x + 4
DIF: Average
17. ANS:
Vertex: 2, 3ÊËÁÁ ˆ
¯˜̃; focus: 2, 5Ê
ËÁÁ ˆ
¯˜̃ ; directrix:y = 1; axis of symmetry:x = 2
18. ANS: H
19. ANS:
12i 6
DIF: Average
20. ANS:
x = −2, y =1
5
DIF: Average
21. ANS: 10 + 20i
DIF: Basic
22. ANS:
3 10
DIF: Basic
23. ANS: –6 – 4i
DIF: Average
ID: C
3
24. ANS: 9 + 18i
DIF: Basic
25. ANS: –9
DIF: Average
26. ANS: 10
29 +
33
29i
DIF: Average
27. ANS: 6
7
DIF: Basic
28. ANS:
35
7
DIF: Average
29. ANS:
DIF: Average
30. ANS: (−3, − 4) and (1, 4)
DIF: Average
31. ANS: D
ID: C
4
32. ANS:
y = 0.1x2
− 9.5x + 245
about 295 hundred meters
DIF: Advanced
33. ANS:
f(x) = −x2
+ 4x − 2
DIF: Advanced
ID: C Algebra 2 - Unit 2 Test [Answer Strip]
_____ 6.H
_____14.F
_____15.A
_____18.H
_____31.D
Name: ________________________ Class: ___________________ Date: __________ ID: D
1
Algebra 2 - Unit 2 Test
1. Factor 15x3
− 6x2
− 25x + 10 by grouping.
2. Factor the trinomial z2
+ 14z + 45.
3. Factor 2x2
− 11x + 15.
4. Factor the trinomial 20y2
− 7y − 40.
5. The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry through the focus,
with endpoints on the parabola. Find the length of the latus rectum of the parabola y =1
8x
2.
____ 6. Identify the axis of symmetry for the graph of f(x) = 2x2
− 8x + 6.
F. y = 2 H. x = −2
G. y = −2 J. x = 2
7. Find the zeros of the function h x( ) = x2
− 27x − 90 by factoring.
8. A quadratic equation has the following coefficients: a = 1, b = 4, and c = 9. Write the solution(s) of the equation.
9. Solve the equation 7x2
+ 63 = 0.
Name: ________________________ ID: D
2
10. Write a quadratic function in standard form with zeros 6 and –4.
11. Solve the equation x2
= 28 − 12x by completing the square.
12. Write the equation in standard form for the parabola with vertex (0,0) and directrix y = −15.
13. Solve x2
= 16 using square roots.
____ 14. Solve 3x2 + x – 5 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.
F. x ≈ 0.30 or x ≈ –2.30 H. There are no solutions.
G. x ≈ 6.81 or x ≈ –8.81 J. x ≈ 1.14 or x ≈ –1.47
____ 15. Find the discriminant of −5x2
+ 5x + 5 = 0.
A. 100 C. 127
B. 126 D. 125
16. Write a quadratic function that fits the points (0, 7), (2, 3), and (4, 7).
Name: ________________________ ID: D
3
17. For the equation x2
+ 8x + 4y + 8 = 0 find the coordinates of the vertex and focus, and the equations of the
directrix and the axis of symmetry. Then graph the equation.
____ 18. Write the equation of the parabola y = x2
+ 4x − 46 in standard form.
F. y + 46 = x + 2( )2
H. y + 50 = x + 2( )2
G. y + 4 = x + 2( )2
J. y + 2 = x + 2( )2
19. Express 6 −68 in terms of i.
20. Find the values of x and y that make the equation 2x + 10i = 14 + (40y)i true.
21. Find the complex conjugate of 5i − 19.
22. Find the absolute value 4 − 5i| |.
23. Add. Write the result in the form a + bi.
(4 – 8i) + (–1 – 7i)
Name: ________________________ ID: D
4
24. Multiply 4i 2 − 6i( ). Write the result in the form a + bi.
25. Simplify −4i26
.
26. Simplify 4 + 3i
−4 − 4i.
27. Simplify the expression 48
75.
28. Simplify 5
6 by rationalizing the denominator.
29. Graph y ≥ x2
− 5x + 4.
Name: ________________________ ID: D
5
30. Solve −8x + 4y = 0
y + 7 = (x + 2)2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
.
____ 31. Graph the system.
x2
+ y2
≤ 9
y ≤ 5 − x2
A. C.
B. D.
Name: ________________________ ID: D
6
32. The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds
x (miles per hour).
Speed, x
(mi/h)
60 65 70 75 80 85 90 95 100
Distance, y
(100 m)
35 50 70 95 125 160 200 245 295
Find an equation of the quadratic function that models the data, and predict the stopping distance for the train
traveling at 105 miles per hour.
33. What quadratic function does the graph represent?
ID: D
1
Algebra 2 - Unit 2 TestAnswer Section
1. ANS:
(5x − 2)(3x2
− 5)
DIF: Average
2. ANS: z + 5( ) z + 9( )
DIF: Basic
3. ANS: x − 3( ) 2x − 5( )
DIF: Basic
4. ANS: (4y + 5)(5y − 8)
DIF: Advanced
5. ANS: 8
DIF: Advanced
6. ANS: J DIF: Average
7. ANS: x = 30 or x = −3
DIF: Basic
8. ANS: –2, –2
9. ANS: x = ±3i
DIF: Average
10. ANS:
f(x) = x2
− 2x − 24
DIF: Average
11. ANS: x = 2 or x = –14
DIF: Basic
12. ANS:
y =1
60x
2
DIF: Average
ID: D
2
13. ANS: The solutions are 4 and –4.
DIF: Basic
14. ANS: J DIF: Average
15. ANS: D
16. ANS:
f x( ) = x2
− 4x + 7
DIF: Average
17. ANS:
Vertex: −4, 2ÊËÁÁ ˆ
¯˜̃ ; focus: −4, 1Ê
ËÁÁ ˆ
¯˜̃; directrix:y = 3; axis of symmetry: x = − 4
18. ANS: H
19. ANS:
12i 17
DIF: Average
20. ANS:
x = 7, y =1
4
DIF: Average
21. ANS: −19 − 5i
DIF: Basic
22. ANS:
41
DIF: Basic
23. ANS: 3 – 15i
DIF: Average
ID: D
3
24. ANS: 24 + 8i
DIF: Basic
25. ANS: 4
DIF: Average
26. ANS:
−7
8 +
1
8i
DIF: Average
27. ANS: 4
5
DIF: Basic
28. ANS:
30
6
DIF: Average
29. ANS:
DIF: Average
30. ANS: (−3, − 6) and (1, 2)
DIF: Average
31. ANS: C
ID: D
4
32. ANS:
y = 0.1x2
− 9.5x + 245
about 350 hundred meters
DIF: Advanced
33. ANS:
f(x) = −x2
+ 8x − 14
DIF: Advanced
ID: D Algebra 2 - Unit 2 Test [Answer Strip]
_____ 6.J
_____14.J
_____15.D
_____18.H
_____31.C
Name: ________________________ Class: ___________________ Date: __________ ID: E
1
Algebra 2 - Unit 2 Test
1. Factor 15x3
− 6x2
− 25x + 10 by grouping.
2. Factor the trinomial x2
+ 14x + 45.
3. Factor 2x2
− 13x + 15.
4. Factor the trinomial 6n2
− 11n − 10.
5. The latus rectum of a parabola is the line segment perpendicular to the axis of symmetry through the focus,
with endpoints on the parabola. Find the length of the latus rectum of the parabola y =1
28x
2.
____ 6. Identify the axis of symmetry for the graph of f(x) = 2x2
+ 4x + 2.
F. y = 0 H. x = −1
G. y = −1 J. x = 0
7. Find the zeros of the function h x( ) = x2
+ 33x + 90 by factoring.
8. A quadratic equation has the following coefficients: a = 2, b = –1, and c = –2. Write the solution(s) of the equation.
9. Solve the equation 3x2
+ 75 = 0.
Name: ________________________ ID: E
2
10. Write a quadratic function in standard form with zeros 8 and –5.
11. Solve the equation x2
= 45 − 12x by completing the square.
12. Write the equation in standard form for the parabola with vertex (0,0) and directrix y = −16.
13. Solve x2
= 100 using square roots.
____ 14. Solve 3x2 + 4x – 2 = 0 using the Quadratic Formula. If necessary, round to the nearest hundredth.
F. x ≈ 2.32 or x ≈ –10.32 H. x ≈ 0.39 or x ≈ –1.72
G. x ≈ –2.95 or x ≈ –5.05 J. There are no solutions.
____ 15. Find the discriminant of 2x2
+ x − 6 = 0.
A. 48 C. 50
B. 49 D. 51
16. Write a quadratic function that fits the points (0, 5), (2, 5), and (3, 8).
Name: ________________________ ID: E
3
17. For the equation x2
− 6x + 8y − 31 = 0 find the coordinates of the vertex and focus, and the equations of the
directrix and the axis of symmetry. Then graph the equation.
____ 18. Write the equation of the parabola y = x2
− 6x − 68 in standard form.
F. y − 3 = x − 3( )2
H. y + 9 = x − 3( )2
G. y + 68 = x − 3( )2
J. y + 77 = x − 3( )2
19. Express 3 −70 in terms of i.
20. Find the values of x and y that make the equation −4x + 7i = 28 + (21y)i true.
21. Find the complex conjugate of 20i + 12.
22. Find the absolute value −7 + 6i| |.
23. Add. Write the result in the form a + bi.
(–8 – 8i) + (–6 – 4i)
Name: ________________________ ID: E
4
24. Multiply 2i 6 − 2i( ). Write the result in the form a + bi.
25. Simplify 11i15
.
26. Simplify 1 − 4i
−1 − 5i.
27. Simplify the expression 50
98.
28. Simplify 3
2 by rationalizing the denominator.
29. Graph y ≤ −2x2
+ x − 3.
Name: ________________________ ID: E
5
30. Solve −8x + 4y = 12
y + 8 = (x + 4)2
Ï
Ì
Ó
ÔÔÔÔÔÔÔÔÔÔÔÔÔÔ
.
____ 31. Graph the system.
x2
+ y2
≤ 9
y ≤ 8 − x2
A. C.
B. D.
Name: ________________________ ID: E
6
32. The table below gives the stopping distance y (in 100 meters) for a train traveling on a track at various speeds
x (miles per hour).
Speed, x
(mi/h)
60 65 70 75 80 85 90 95 100
Distance, y
(100 m)
35 50 70 95 125 160 200 245 295
Find an equation of the quadratic function that models the data, and predict the stopping distance for the train
traveling at 105 miles per hour.
33. What quadratic function does the graph represent?
ID: E
1
Algebra 2 - Unit 2 TestAnswer Section
1. ANS:
(5x − 2)(3x2
− 5)
DIF: Average
2. ANS: x + 5( ) x + 9( )
DIF: Basic
3. ANS: x − 5( ) 2x − 3( )
DIF: Basic
4. ANS: (2n − 5)(3n + 2)
DIF: Advanced
5. ANS: 28
DIF: Advanced
6. ANS: H DIF: Average
7. ANS: x = −30 or x = −3
DIF: Basic
8. ANS: 1.28, –0.78
9. ANS: x = ±5i
DIF: Average
10. ANS:
f(x) = x2
− 3x − 40
DIF: Average
11. ANS: x = 3 or x = –15
DIF: Basic
12. ANS:
y =1
64x
2
DIF: Average
ID: E
2
13. ANS: The solutions are 10 and –10.
DIF: Basic
14. ANS: H DIF: Average
15. ANS: B
16. ANS:
f x( ) = x2
− 2x + 5
DIF: Average
17. ANS:
Vertex: 3, 5ÊËÁÁ ˆ
¯˜̃; focus: 3, 3Ê
ËÁÁ ˆ
¯˜̃ ; directrix:y = 7; axis of symmetry:x = 3
18. ANS: J
19. ANS:
3i 70
DIF: Average
20. ANS:
x = −7, y =1
3
DIF: Average
21. ANS: 12 − 20i
DIF: Basic
22. ANS:
85
DIF: Basic
23. ANS: –14 – 12i
DIF: Average
ID: E
3
24. ANS: 4 + 12i
DIF: Basic
25. ANS: –11i
DIF: Average
26. ANS: 19
26 +
9
26i
DIF: Average
27. ANS: 5
7
DIF: Basic
28. ANS:
6
2
DIF: Average
29. ANS:
DIF: Average
30. ANS: (−5, − 7) and (−1, 1)
DIF: Average
31. ANS: C
ID: E
4
32. ANS:
y = 0.1x2
− 9.5x + 245
about 350 hundred meters
DIF: Advanced
33. ANS:
f(x) = −x2
+ 10x − 24
DIF: Advanced
ID: E Algebra 2 - Unit 2 Test [Answer Strip]
_____ 6.H
_____14.H
_____15.B
_____18.J
_____31.C