1.2.1 minimum value. 1.2.2 minimum = -9 if x = 0
1.3 AO = 3, OB = 3, OC = 9, AB = 6 and AC = 9,487
1.4.1 y = 7 1.4.2 y = 11,25
1.5.1 x = -2 or x = +2 1.5.2 x = -3,742 or x = 4,742
1.6.1 x = -3 or x = +3 1.6.2 -3 < x < 3 1.6.3 x < -3 or x > 3
2.1 A(-4 ; 0), B(4 ; 0) and C(0 ; -16)
2.2.1 minimum value. 2.2.2 minimum = -16 if x = 0
2.3 AO = 4, OB = 4, OC = 16, AB = 8 and AC = 16,492
2.4.1 y = -7 2.4.2 y = -15
2.5.1 x = -2,449 or x = +2,449 2.5.2 x = -4,583 or x = 4,583
2.6.1 x = -4 or x = +4 2.6.2 -4 < x < 4 2.6.3 x < -4 or x > 4
3.1 A(-4 ; 0), B(4 ; 0) and C(0 ; 16)
3.2.1 maximum value. 3.2.2 maximum = 16 if x = 0
3.3 AO = 4, OB = 4, OC = 16, AB = 8 and AC = 16,492
3.4.1 y = 7 3.4.2 y = 13,75
3.5.1 x = -4,583 or x = 4,583 3.5.2 x = -2,449 or x = 2,449
3.6.1 x = -4 or x = 4 3.6.2 x < -4 or x > 4 3.6.3 -4 < x < 4
4.1 A(-8 ; 0), B(8 ; 0) and C(0 ; 64)
4.2.1 maximum value. 4.2.2 maximum = 64 if x = 0
4.3 AO = 8, OB = 8, OC = 64, AB = 16 and AC = 64,498
4.4.1 y = 39 4.4.2 y = 55
4.5.1 x = -7,348 or x = 7,348 4.5.2 x = -6,633 or x = 6,633
4.6.1 x = -8 or x = 8 4.6.2 x < -8 or x > 8 4.6.3 -8 < x < 8
5.1 A(-2 ; 0), B(2 ; 0), C(0 ; -4) 5.2 See graph to the right.
5.3 p = -0,938
q = 2,646 or q = -2,646
6.1 A(-5 ; 0), B(5 ; 0), C(0 ; -25) 6.2 See graph to the right.
6.3 p = -6,51
q = -3,162 or q = 3,162
7.1 A(-6 ; 0), B(6 ; 0), C(0 ; 36) 7.2 See graph to the right.
7.3 p = 17,938
q = -5,099 or q = 5,099
8.1 A(-7 ; 0), B(7 ; 0), C(0 ; 49) 8.2 See graph to the right.
8.3 p = 34,56
q = -5,099 or q = 5,099
9.1 y = x² - 16 c = -16
9.2 D(0 ; -16)
9.3 P(-3 ; -7), Q(3 ; -7), M(0 ; -7)
9.4 AO = 4; OB = 4; OD = 16; PM = 3; MQ = 3; AB = 8; PQ = 6;
OM = 7; MD = 9; PD = 9,487; OQ = 7,616
9.5.1 x = -4 or x = 4 9.5.2 -4 < x < 4 9.5.3 x < -4 or x > 4
9.5.4 x = -3 or x = 3 9.5.5 -3 < x < 3 9.5.6 x < -3 or x > 3
10.1 y = x² - 169 c = -169
10.2 D(0 ; -169)
10.3 P(6 ; -133), Q(-6 ; -133), M(0 ; -133)
10.4 AO = 13; OB = 13; OC = 169; PM = 6; MQ = 6; AB = 26; PQ = 12;
OM = 133; MC = 36; PC = 36,497; OQ = 133,135
10.5.1 x = -13 or x = 13 10.5.2 -13 < x < 13 10.5.3 x < -13 or x > 13
10.5.4 x = -6 or x = 6 10.5.5 -6 < x < 6 10.5.6 x < -6 or x > 6
10.5.7 -13 < x < -6 or 6 < x < 13
11.1 y = 144 - x² c = 144
11.2 D(0 ; 144)
11.3 P(-8 ; 80), Q(8 ; 80), M(0 ; 80)
11.4 AO = 12; OB = 12; OC = 144; PM = 8; MQ = 8; AB = 24; PQ = 16;
OM = 80; MC = 64; PC = 64,498; OQ = 80,399
11.5.1 x = -12 or x = 12 11.5.2 x < -12 or x > 12 11.5.3 -12 < x < 12
11.5.4 x = -8 or x = 8 11.5.5 x < -8 or x > 8 11.5.6 -8 < x < 8
11.5.7 -12 < x < -8 or 8 < x < 12
12.1 y = 81 - x² c = 81
12.2 D(0 ; 81)
12.3 P(-7 ; 32), Q(7 ; 32), M(0 ; 32)
12.4 AO = 9; OB = 9; OC = 81; PM = 7; MQ = 7; AB = 18; PQ = 14;
OM = 32; MC = 49; PC = 49,497; OQ = 32,757
12.5.1 x = -9 or x = 9 12.5.2 x < -9 or x > 9 12.5.3 -9 < x < 9
12.5.4 x = -7 or x = 7 12.5.5 x < -7 or x > 7 12.5.6 -7 < x < 7
12.5.7 -9 < x < -7 or 7 < x < 9
13.1 A(-4 ; 0) O(0 ; 0)
13.2 C(-2 ; -4)
13.3 minimum value = -4
13.4 AO = 4
13.5 c = -2
13.6.1 x = -4 or x = 0 13.6.2 -4 < x < 0 13.6.3 x < -4 or x > 0
14.1 O(0 ; 0) B(4 ; 0)
14.2 C(2 ; -4)
14.3 minimum value = -4
14.4 OB = 4
14.5 c = 2
14.6.1 x = 0 or x = 4 14.6.2 0 < x < 4 14.6.3 x < 0 or x > 4
15.1 O(0 ; 0) B(4 ; 0)
15.2 C(2 ; 4)
15.3 maximum value = 4
15.4 OB = 4
15.5 c = 2
15.6.1 x = 0 or x = 4 15.6.2 x < 0 or x > 4 15.6.3 0 < x < 4
16.1 y = x² + 6x
16.2 M(-3 ; 0) MC: x = -3
16.3 C(-3 ; -9)
16.4 minimum value = -9
16.5 AO = 6; AM = 3; MO = 3; MC = 9
16.6.1 x = -6 or x = 0 16.6.2 -6 < x < 0 16.6.3 x < -6 or x > 0
17.1 M(4 ; 0) B(8 ; 0)
17.2 y = x² - 8x c = -8
17.3 C(4 ; -16) minimum value = -16
17.4 MC = 16
17.5.1 x = 0 or x = 8 17.5.2 0 < x < 8 17.5.3 x < 0 or x > 8
18.1 y = 10x - x² c = 10
18.2 M(5 ; 0) MC : x = 5
18.3 C)5 ; 25)
18.4 maximum = 25
18.5 AO = 10; AM = 5; MO = 5; MC = 25
18.6.1 x = 0 or x = 10 18.6.2 x < 0 or x > 10 18.6.3 0 < x < 10
19.1 A(-15 ; 0) M(-7,5 ; 0) T (-7,5 ; 56,25)
19.2 y = -x² - 15x or y = -(x² + 15x)
19.3 p = 44
19.4 q = -1
19.5 y = mx + c
P(-11;44): 44 = m(-11) + c
44 = -11m + c ... (1)
Q(-1 ;14): 14 = m(-1) + c
14 = -m + c ... (2)
From (2) : 14 + m = c
Into (1) : 44 = -11m + 14 + m
30 = -10m
-3 = m
Into (2) : 14 = -(-3) + c
11 = c
y = -3x + 11
19.6.1 x < -15 or x < 0 19.6.2 -15 < x < 0 19.6.3 x < 3,667
19.6.4 x = 3,667 19.6.5 x < -11 or x > -1 19.6.6 -11 < x < -1
20.1 A(9 ; 0) M(4,5 ; 0) T (4,5 ; 20,25)
20.2 OA = 9; MA = 4,5; MT = 20,25
20.3 p = 10,01
20.4 q = 6,5
20.5 (2,5 ; 16,25)
20.6 y = 1,2x + 8,45
20.7.1 x < 0 or x > 9 20.7.2 0 < x < 9 20.7.3 x < -7,042
20.7.4 x = -7,042 20.7.5 x < 1,3 or x > 6,5 20.7.6 1,3 < x < 6,5