Graad 10 - Nog Oefeninge : Antwoorde.
Die parabool
1.1 A(-3 ; 0), B(3 ; 0) and C(0 ; -9)
1.2.1 minimum waarde.
1.2.2 minimum = -9 as x = 0
1.3 AO = 3, OB = 3, OC = 9, AB = 6 en AC = 9,487
1.4.1 y = 7
1.4.2 y = 11,25
1.5.1 x = -2 of x = +2
1.5.2 x = -3,742 of x = 4,742
1.6.1 x = -3 of 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 waarde.
2.2.2 minimum = -16 as x = 0
2.3 AO = 4, OB = 4, OC = 16, AB = 8 en AC = 16,492
2.4.1 y = -7
2.4.2 y = -15
2.5.1 x = -2,449 of x = +2,449
2.5.2 x = -4,583 of x = 4,583
2.6.1 x = -4 of x = +4
2.6.2 -4 < x < 4
2.6.3 x < -4 of x > 4
3.1 A(-4 ; 0), B(4 ; 0) en C(0 ; 16)
3.2.1 maksimum waarde.
3.2.2 maksimum = 16 as x = 0
3.3 AO = 4, OB = 4, OC = 16, AB = 8 en AC = 16,492
3.4.1 y = 7
3.4.2 y = 13,75
3.5.1 x = -4,583 of x = 4,583
3.5.2 x = -2,449 of x = 2,449
3.6.1 x = -4 of x = 4
3.6.2 x < -4 of x > 4
3.6.3 -4 < x < 4
4.1 A(-8 ; 0), B(8 ; 0) en C(0 ; 64)
4.2.1 maksimum waarde.
4.2.2 maksimum = 64 as x = 0
4.3 AO = 8, OB = 8, OC = 64, AB = 16 en AC = 64,498
4.4.1 y = 39
4.4.2 y = 55
4.5.1 x = -7,348 of x = 7,348
4.5.2 x = -6,633 of x = 6,633
4.6.1 x = -8 of x = 8
4.6.2 x < -8 of x > 8
4.6.3 -8 < x < 8
5.1 A(-2 ; 0), B(2 ; 0), C(0 ; -4)
5.2 Kyk na meegaande grafiek.
5.3 p = -0,938
q = 2,646 of q = -2,646
6.1 A(-5 ; 0), B(5 ; 0), C(0 ; -25)
6.2 Kyk na meegaande grafiek.
6.3 p = -6,51
q = -3,162 of q = 3,162
7.1 A(-6 ; 0), B(6 ; 0), C(0 ; 36)
7.2 Sien meegaande grafiek.
7.3 p = 17,938
q = -5,099 of q = 5,099
8.1 A(-7 ; 0), B(7 ; 0), C(0 ; 49)
8.2 Sien meegaande grafiek.
8.3 p = 34,56
q = -5,099 of 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 of x = 4
9.5.2 -4 < x < 4
9.5.3 x < -4 of x > 4
9.5.4 x = -3 of x = 3
9.5.5 -3 < x < 3
9.5.6 x < -3 of 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 of x = 13
10.5.2 -13 < x < 13
10.5.3 x < -13 of x > 13
10.5.4 x = -6 of x = 6
10.5.5 -6 < x < 6
10.5.6 x < -6 of x > 6
10.5.7 -13 < x < -6 of 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 of x = 12
11.5.2 x < -12 of x > 12
11.5.3 -12 < x < 12
11.5.4 x = -8 of x = 8
11.5.5 x < -8 of x > 8
11.5.6 -8 < x < 8
11.5.7 -12 < x < -8 of 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 of x = 9
12.5.2 x < -9 of x > 9
12.5.3 -9 < x < 9
12.5.4 x = -7 of x = 7
12.5.5 x < -7 of x > 7
12.5.6 -7 < x < 7
12.5.7 -9 < x < -7 of 7 < x < 9
13.1 A(-4 ; 0) O(0 ; 0)
13.2 C(-2 ; -4)
13.3 minimum waarde = -4
13.4 AO = 4
13.5 c = -2
13.6.1 x = -4 of x = 0
13.6.2 -4 < x < 0
13.6.3 x < -4 of x > 0
14.1 O(0 ; 0) B(4 ; 0)
14.2 C(2 ; -4)
14.3 minimum waarde = -4
14.4 OB = 4
14.5 c = 2
14.6.1 x = 0 of x = 4
14.6.2 0 < x < 4
14.6.3 x < 0 of x > 4
15.1 O(0 ; 0) B(4 ; 0)
15.2 C(2 ; 4)
15.3 maksimum waarde = 4
15.4 OB = 4
15.5 c = 2
15.6.1 x = 0 of x = 4
15.6.2 x < 0 of 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 waarde = -9
16.5 AO = 6;
AM = 3;
MO = 3;
MC = 9
16.6.1 x = -6 of x = 0
16.6.2 -6 < x < 0
16.6.3 x < -6 of x > 0
17.1 M(4 ; 0) B(8 ; 0)
17.2 y = x² - 8x c = -8
17.3 C(4 ; -16) minimum waarde = -16
17.4 MC = 16
17.5.1 x = 0 of x = 8
17.5.2 0 < x < 8
17.5.3 x < 0 of x > 8
18.1 y = 10x - x² c = 10
18.2 M(5 ; 0) MC : x = 5
18.3 C)5 ; 25)
18.4 maksimum = 25
18.5 AO = 10;
AM = 5;
MO = 5;
MC = 25
18.6.1 x = 0 of x = 10
18.6.2 x < 0 of 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 of 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)
Van (2) : 14 + m = c
In (1) : 44 = -11m + 14 + m
30 = -10m
-3 = m
In (2) : 14 = -(-3) + c
11 = c
y = -3x + 11
19.6.1 x < -15 of 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 of 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 of 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 of x > 6,5
20.7.6 1,3 < x < 6,5