Algebra 2 - Task 3.12
Name___________________________________
Unit 3 - Qudratics Review
Date________________ Period____
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Part 1 - Find the discriminant of each quadratic equation then state the number and type of solutions. How does this connect to the graph? 1) 8n 2 − 8 = 0
2) −6b 2 + 7b + 5 = 0
Part 2 - Solve each equation by factoring. 3) x 2 = 5 x + 6
4) a 2 − 6a = 16
5) v 2 − 25 = 0
6) n 2 + 7n = −10
7) 2 x 2 + 30 = −17 x
8) 3k 2 = −4k − 1
9) 2n 2 = −3n
10) 3 x 2 + 64 = 32 x
Part 3 - Solve each equation by taking square roots. 11) n 2 − 10 = 2
12) −7m 2 = −378
13) p 2 − 10 = 63
14) x 2 + 1 = 93
Part 4 - Solve each equation by completing the square. 15) b 2 − 14b + 40 = 0
16) r 2 + 4r − 32 = 0
17) 2 x 2 + 16 x − 96 = 0
18) 4n 2 + 16n − 9 = 0
19) 4v 2 + 16v − 76 = 8
20) 10b 2 − 20b − 19 = −4
21) 10v 2 = 80 + 20v
22) 7b 2 = 9 + 14b
Part 5 - Solve each equation with the quadratic formula. 23) 4 x 2 + 2 x + 8 = 0
24) 4 x 2 + 11 x − 23 = 0
25) 2 x 2 − 5 x − 7 = 2
26) k 2 − 3k − 6 = −3
27) 2a 2 + a − 10 = −3
28) p 2 + 5 p − 18 = −4
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-1-
Worksheet by Kuta Software LLC
Part 6 - Sketch the graph of each function. 29) f (x) = −2 x 2 − 12 x − 19 −6
−5
−4
−3
−2
−1 0 −1
1
2
30) f (x) = − x 2 + 2 x − 4 3
4
−5
−4
−3
−2
−1
0
1
2
3
−1
−2 −2 −3 −3
−4 −5
−4
−6
−5
−7 −6 −8 −7
−9 −10
−8
2
2
31) f (x) = −( x + 3) − 3 −5
−4
−3
−2
−1
0
32) f (x) = 2( x + 2) + 4 1
2
3
12
−1 −2
10
−3
8
−4
6
−5 4 −6 2
−7 −8
−10
−8
−6
−4
−2
0
33) What is the discriminant and why is it important?
34) What does "a" tell you about the graph of a quadratic function? Give examples.
35) Challenge - Write the equation of f (x) = x 2 but is shifted to the left 6 units and flipped over the x-axis.
36) What is the definition of a function?
Part 7 - Simplify. 37) (−2 + 4i) − (2 + i)
38) (5i) − 5 + (7 + 8i)
39) (−3 − 8i) + (−5 − 8i)
40) −2 − (5i) + (−4 + 6i)
41) (−5i)(−6 − 6i)
42) (5i)(−8i)
43) (6 + 2i) 45)
2
−9 − i −6i
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44) (−1 + 2i)(7 + 6i) 46)
-2-
−3 + 10i 4i
Worksheet by Kuta Software LLC
47)
6 + 10i −2i
48)
−8 − i i
49)
−4 + 9i −3 − 4i
50)
4 + 8i 2 − 4i
51)
7 − 8i −7 − 10i
52)
6 − 2i −10 + 7i
53) (i) 23
54) (i) 74
Part 8- Graph each number in the complex plane. 55) −3 − i
56) 4 + 2i Imaginary
Imaginary
Real
Real
57) 0
58) −4 + 4i Imaginary
Imaginary
Real
Real
Part 9 - Identify each complex number graphed. 59)
60)
Imaginary
Real
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Imaginary
Real
-3-
Worksheet by Kuta Software LLC
Algebra 2 - Task 3.12
Name___________________________________
Unit 3 - Qudratics Review
Date________________ Period____
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Part 1 - Find the discriminant of each quadratic equation then state the number and type of solutions. How does this connect to the graph? 1) 8n 2 − 8 = 0 256; two real solutions
2) −6b 2 + 7b + 5 = 0 169; two real solutions
Part 2 - Solve each equation by factoring. 3) x 2 = 5 x + 6
{−1, 6}
4) a 2 − 6a = 16
5) v 2 − 25 = 0
{−5, 5}
6) n 2 + 7n = −10
{ { }
9) 2n 2 = −3n
{−5, −2}
8) 3k 2 = −4k − 1
{
3, −2 3 }
12) −7m 2 = −378
{3
73, − 73 }
14) x 2 + 1 = 93
5 − , −6 2
7) 2 x 2 + 30 = −17 x
}
{8, −2}
} { }
1 − , −1 3 8 2 10) 3 x + 64 = 32 x ,8 3
3 − ,0 2
Part 3 - Solve each equation by taking square roots. 11) n 2 − 10 = 2 13) p 2 − 10 = 63
{2 {
{2
6, −3 6 } 23, −2 23 }
Part 4 - Solve each equation by completing the square. 15) b 2 − 14b + 40 = 0 17) 2 x 2 + 16 x − 96 = 0
{4, −12}
19) 4v 2 + 16v − 76 = 8
{3, −7}
21) 10v 2 = 80 + 20v
16) r 2 + 4r − 32 = 0
{10, 4}
{4, −8}
{ }
1 9 ,− 2 2 2+ 20) 10b 2 − 20b − 19 = −4 18) 4n 2 + 16n − 9 = 0
22) 7b 2 = 9 + 14b
{4, −2}
{
{
10 2 − ,
2 7+4 7 7−4 7 , 7 7
}
10 2
}
Part 5 - Solve each equation with the quadratic formula. −1 + i 31 −1 − i 31 −11 + 489 −11 − 489 23) 4 x 2 + 2 x + 8 = 0 , 24) 4 x 2 + 11 x − 23 = 0 , 4 4 8 8 5 + 97 5 − 97 3 + 21 3 − 21 25) 2 x 2 − 5 x − 7 = 2 , 26) k 2 − 3k − 6 = −3 , 4 4 2 2 −1 + 57 −1 − 57 27) 2a 2 + a − 10 = −3 , 28) p 2 + 5 p − 18 = −4 {2, −7} 4 4
{ { {
}
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}
{
}
-1-
{
}
}
Worksheet by Kuta Software LLC
Part 6 - Sketch the graph of each function. 29) f (x) = −2 x 2 − 12 x − 19 −6
−5
−4
−3
−2
−1 0 −1
1
2
30) f (x) = − x 2 + 2 x − 4 3
4
−5
−4
−3
−2
−1
0
1
2
3
−1
−2 −2 −3 −3
−4 −5
−4
−6
−5
−7 −6 −8 −7
−9 −10
−8
2
2
31) f (x) = −( x + 3) − 3 −5
−4
−3
−2
−1
0
32) f (x) = 2( x + 2) + 4 1
2
3
12
−1 −2
10
−3
8
−4
6
−5 4 −6 2
−7 −8
−10
−8
−6
−4
−2
0
33) What is the discriminant and why is it 34) What does "a" tell you about the graph of a important? quadratic function? Give examples. The dot next to the choice indicates that it is the answer. The dot next to the choice indicates that it is the answer. 36) What is the definition of a function? 35) Challenge - Write the equation of f (x) = x 2 The dot next to the choice indicates that it is the answer. but is shifted to the left 6 units and flipped over the x-axis. The dot next to the choice indicates that it is the answer. Part 7 - Simplify. 37) (−2 + 4i) − (2 + i) −4 + 3i
38) (5i) − 5 + (7 + 8i) 2 + 13i
39) (−3 − 8i) + (−5 − 8i) −8 − 16i
40) −2 − (5i) + (−4 + 6i) −6 + i
41) (−5i)(−6 − 6i) −30 + 30i
42) (5i)(−8i) 40
43) (6 + 2i) 45)
2
32 + 24i
−9 − i −9i + 1 −6i 6
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44) (−1 + 2i)(7 + 6i) −19 + 8i 46)
-2-
−3 + 10i 3i + 10 4i 4
Worksheet by Kuta Software LLC
47)
6 + 10i 3i − 5 −2i
48)
−8 − i 8i − 1 i
49)
−4 + 9i −24 − 43i −3 − 4i 25
50)
4 + 8i −6 + 8i 2 − 4i 5
51)
7 − 8i 31 + 126i −7 − 10i 149
52)
6 − 2i −74 − 22i −10 + 7i 149
53) (i) 23 -i Part 8- Graph each number in the complex plane.
54) (i) 74 -1
55) −3 − i
56) 4 + 2i Imaginary
Imaginary
Real
Real
57) 0
58) −4 + 4i Imaginary
Imaginary
Real
Real
Part 9 - Identify each complex number graphed. 59)
3 − 4i
Imaginary
60)
Real
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−1 − 5i
Imaginary
Real
-3-
Worksheet by Kuta Software LLC
