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