Quadratics
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ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJAK
1
abcQuadratic
discrim.
axis
extremum
Vertex
Vertex-form
x1x2discrim
2
3
1949x4 x² + 9x + 465-4.54( -4.5, 4 )
(x - -4.5)² - 4
622
4
5
6
100 000( 0, 0 )(x - 0)²000
7
110 x x² + x1-0.50( -0.5, 0 )(x - -0.5)²111
8
111 x1 x² + x + 1-3-0.51( -0.5, 1 )
(x - -0.5)² - 1
11.00-0.5 + 1 i-0.5 - 1 i
9
00
10
1212x1 x² + 2x + 10-11( -1, 1 )(x - -1)² - 10-1-1
11
1323x2 x² + 3x + 21-1.52( -1.5, 2 )
(x - -1.5)² - 2
1-1-1
12
1434x3 x² + 4x + 34-23( -2, 3 )(x - -2)² - 31-1-1
13
3543x²5x4
3x² + 5x + 4
-23-0.8334( -0.833, 4 )
(x - -0.833)² - 4
22.00-0.833 + 2 i-0.833 - 2 i
14
00
15
111 x1 x² + x + 1-3-0.51( -0.5, 1 )
(x - -0.5)² - 1
11.00-0.5 + 1 i-0.5 - 1 i
16
1212x1 x² + 2x + 10-11( -1, 1 )(x - -1)² - 10-1-1
17
1313x1 x² + 3x + 15-1.51( -1.5, 1 )
(x - -1.5)² - 1
211
18
1414x1 x² + 4x + 112-21( -2, 1 )(x - -2)² - 1200
19
1515x1 x² + 5x + 121-2.51( -2.5, 1 )
(x - -2.5)² - 1
311
20
1616x1 x² + 6x + 132-31( -3, 1 )(x - -3)² - 1411
21
1717x1 x² + 7x + 145-3.51( -3.5, 1 )
(x - -3.5)² - 1
522
22
1818x1 x² + 8x + 160-41( -4, 1 )(x - -4)² - 1511
23
1919x1 x² + 9x + 177-4.51( -4.5, 1 )
(x - -4.5)² - 1
622
24
110110x1
x² + 10x + 1
96-51( -5, 1 )(x - -5)² - 1722
25
00
26
101 1 x² + 1-401( 0, 1 )(x - 0)² - 111.000 + 1 i0 - 1 i
27
1-10-1x x² + -1x10.50( 0.5, 0 )(x - 0.5)²122
28
1-2-1-2x-1
x² + -2x + -1
81-1( 1, -1 )x233
29
1-3-2-3x-2
x² + -3x + -2
171.5-2( 1.5, -2 )
(x - 1.5)² - -2
355
30
1-4-3-4x-3
x² + -4x + -3
282-3( 2, -3 )(x - 2)² - -3466
31
1-5-4-5x-4
x² + -5x + -4
412.5-4( 2.5, -4 )
(x - 2.5)² - -4
588
32
1-6-5-6x-5
x² + -6x + -5
563-5( 3, -5 )(x - 3)² - -5588
33
1-7-6-7x-6
x² + -7x + -6
733.5-6( 3.5, -6 )
(x - 3.5)² - -6
61010
34
1-8-7-8x-7
x² + -8x + -7
924-7( 4, -7 )(x - 4)² - -771111
35
1-9-8-9x-8
x² + -9x + -8
1134.5-8( 4.5, -8 )
(x - 4.5)² - -8
81313
36
1-10-9-10x-9
x² + -10x + -9
1365-9( 5, -9 )(x - 5)² - -981313
37
00
38
00
39
00
40
1313x1 x² + 3x + 15-1.51( -1.5, 1 )
(x - -1.5)² - 1
211
41
1323x2 x² + 3x + 21-1.52( -1.5, 2 )
(x - -1.5)² - 2
1-1-1
42
1333x3 x² + 3x + 3-3-1.53( -1.5, 3 )
(x - -1.5)² - 3
11.00-1.5 + 1 i-1.5 - 1 i
43
1343x4 x² + 3x + 4-7-1.54( -1.5, 4 )
(x - -1.5)² - 4
22.00-1.5 + 2 i-1.5 - 2 i
44
1353x5 x² + 3x + 5-11-1.55( -1.5, 5 )
(x - -1.5)² - 5
22.00-1.5 + 2 i-1.5 - 2 i
45
1363x6 x² + 3x + 6-15-1.56( -1.5, 6 )
(x - -1.5)² - 6
33.00-1.5 + 3 i-1.5 - 3 i
46
1373x7 x² + 3x + 7-19-1.57( -1.5, 7 )
(x - -1.5)² - 7
33.00-1.5 + 3 i-1.5 - 3 i
47
1383x8 x² + 3x + 8-23-1.58( -1.5, 8 )
(x - -1.5)² - 8
33.00-1.5 + 3 i-1.5 - 3 i
48
1393x9 x² + 3x + 9-27-1.59( -1.5, 9 )
(x - -1.5)² - 9
44.00-1.5 + 4 i-1.5 - 4 i
49
13103x10
x² + 3x + 10
-31-1.510( -1.5, 10 )
(x - -1.5)² - 10
44.00-1.5 + 4 i-1.5 - 4 i
50
00
51
1303x x² + 3x9-1.50( -1.5, 0 )(x - -1.5)²211
52
12-12x-1
x² + 2x + -1
8-1-1( -1, -1 )(x - -1)² - -1211
53
12-22x-2
x² + 2x + -2
12-1-2( -1, -2 )(x - -1)² - -2211
54
12-32x-3
x² + 2x + -3
16-1-3( -1, -3 )(x - -1)² - -3322
55
12-42x-4
x² + 2x + -4
20-1-4( -1, -4 )(x - -1)² - -4322
56
12-52x-5
x² + 2x + -5
24-1-5( -1, -5 )(x - -1)² - -5322
57
12-62x-6
x² + 2x + -6
28-1-6( -1, -6 )(x - -1)² - -6433
58
12-72x-7
x² + 2x + -7
32-1-7( -1, -7 )(x - -1)² - -7433
59
12-82x-8
x² + 2x + -8
36-1-8( -1, -8 )(x - -1)² - -8433
60
12-92x-9
x² + 2x + -9
40-1-9( -1, -9 )(x - -1)² - -9433
61
12-102x-10
x² + 2x + -10
44-1-10( -1, -10 )
(x - -1)² - -10
544
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