1.

a. k = 3p + 18 f. w = 12e - 3e2 b. r = 12a - 8 g. y = -x + 5 c. q = b2 - 4b h. d = -15c - 20 d. y = 24 + 42x i. t = s2 + 5s e. g = -32h - 64 j. k = -8 + 4m

2.

a. k = 5p4 + 40p2 f. w = 35e3 - 21e7 b. r = 35a3 - 28a2 g. y = -x4 + 7x2

c. q = p5 - 8p4 h. d = -40c6 - 24c4

d. y = 18x + 72x3 i. t = w4 + 9w5

e. g = -60h6 - 135h4 j. k = -7n4 + 3n9

3.

a. k = (n - 7)(n + 3) h. n = (3 + 4a)(a + 2) k = n2 + 3n - 7n - 21 n = 3a + 6 + 4a2 + 8a

k = n2 - 4n - 21 n = 4a2 + 11a + 6

b. r = (p + 2)(p - 9) i. y = (x + 9)2

r = p2 - 9p + 2p - 18 y = (x + 9)(x + 9)

r = p2 - 7p - 18 y = x2 + 9x + 9x + 81

y = x2 + 18x + 81

c. y = (x - 1/2)(x + 5) j. h = (t - 4)2

y = x2 + 5x - 1/2x - 212 h = (t - 4)(t - 4)

y = x2 + 41/2x - 21/2 h = t2 - 4t - 4t + 16

h = t2 - 8t + 16

Wiskunde Vwo Deel 3 A Hoofdstuk 4 Vwo 3

Uitwerkingen

d. y = (7 - s)(s + 5) k. h = (7 - g)2

y = 7s + 35 - s2 - 5s h = (7 - g)(7 - g)

y = -s2 + 2s + 35 h = 49 - 7g - 7g + g2

h = g2 - 14g + 49

e. h = (g - 7)(g + 7) l. r = (-p - 7)2

h = g2 + 7g - 7g - 49 r = (-p - 7)(-p - 7)

h = g2 - 49 r = p2 + 7p + 7p + 49

r = p2 + 14p + 49

f. h = (v - 7)(3 + v) m. n = (a + 11)2

h = 3v + v2 - 21 - 7v n = (a + 11)(a + 11)

h = v2 - 4v - 21 n = a2 + 11a + 11a + 121

n = a2 + 22a + 121

g. z = (b + 8)(b + 11) l. v = (-3 - 4h)2

z = b2 + 11b + 8b + 88 v = (-3 - 4h)(-3 - 4h)

z = b2 + 19b + 88 v = 9 + 12h + 12h + 16h2

v = 16h2 + 24h + 9

4.

a. k = (n - 8)(n + 4) h. n = (3 + 5a)(a + 4) k = n2 + 4n - 8n - 32 n = 3a + 12 + 5a2 + 20a

k = n2 - 4n - 32 n = 5a2 + 23a + 12

b. r = (p + 3)(p - 10) i. y = (x + 4)2

r = p2 - 10p + 3p - 30 y = (x + 4)(x + 4)

r = p2 - 7p - 30 y = x2 + 4x + 4x + 16

y = x2 + 8x + 16

c. y = (x - 1/3)(x + 9) j. h = (t - 7)2

y = x2 + 9x - 1/3x - 3 h = (t - 7)(t - 7)

y = x2 + 82/3x - 3 h = t2 - 7t - 7t + 49

h = t2 - 14t + 49

d. y = (8 - s)(s + 7) k. h = (8 - g)2

y = 8s + 56 - s2 - 7s h = (8 - g)(8 - g)

y = -s2 + s + 56 h = 64 - 8g - 8g + g2

h = g2 - 16g + 64

e. h = (g - 9)(g + 9) l. r = (-p - 15)2

h = g2 + 9g - 9g - 81 r = (-p - 15)(-p - 15)

h = g2 - 81 r = p2 + 15p + 15p + 225

r = p2 + 30p + 225

f. h = (v - 8)(4 + v) m. n = (a + 13)2

h = 4v + v2 - 32 - 8v n = (a + 13)(a + 13)

h = v2 - 4v - 32 n = a2 + 13a + 13a + 169

n = a2 + 26a + 169

g. z = (b + 12)(b + 4) l. v = (-4 - 5h)2

z = b2 + 4b + 12b + 48 v = (-4 - 5h)(-4 - 5h)

z = b2 + 16b + 48 v = 16 + 20h + 20h + 25h2

v = 25h2 + 40h + 16

5.

a. n = a(a + 8) g. p = 8(-q + 4) b. j = 15t(t - 5) h. y = 6x(-x + 4)

c. y = 12b(1 + 4b) i. r = -2(4s + 3)

d. e = h(h - 13) j. d = 10e(-1 + 6e)

e. k = 9p(p - 8) k. w = -(6d + 7)

f. y = 7x(4x + 5) l. v = -(8w + 3)

6.

a. n = a(a3 - 12) g. p = 8q(-q2 + 7) b. j = 6t2(3t - 10) h. y = 5x(-x4 + 9)

c. y = 11b(1 + 6b3) i. r = -3(4s2 + 3)

d. e = h2(h3 + 14) j. d = 4e2(-1 + 13e)

e. k = 8p5(p + 9) k. w = -d(11d + 8d3)

f. y = 16x2(2 + 3x) l. v = -w2(2w + 9)

7.

a. (x + 4)(x - 6) = 0 h. (4r - 20)(r - 9) = 0 x + 4 = 0 of x - 6 = 0 4r - 20 = 0 of r - 9 = 0

x = -4 of x = 6 4r = 20 of r = 9

r = 5 of r = 9

b. (m - 6)(m + 12) = 0 i. (2 - q)(q + 0,4) = 0

m - 6 = 0 of m + 12 = 0 2 - q = 0 of q + 0,4 = 0

m = 6 of m = -12 q = 2 of q = -0,4

c. (a - 5)(a + 5) = 0 j. 3w(5w + 9) = 0

a - 5 = 0 of a + 5 = 0 3w = 0 of 5w + 9 = 0

a = 5 of a = -5 w = 0 of 5w = -9

w = 0 of w = -1,8

d. s(s + 7) = 0 k. g(g3 - 64) = 0

s = 0 of s + 7 = 0 g = 0 of g3 - 64 = 0

s = 0 of s = -7 g = 0 of g3 = 64

g = 0 of g = 4

e. (n - 7)(n + 7) = 0 l. (k + 7)(3k - 7) = 0

n - 7 = 0 of n + 7 = 0 k + 7 = 0 of 3k - 7 = 0

n = 7 of n = -7 k = -7 of 3k = 7

k = -7 of k = 2,33

f. (r - 3)(r - 9) = 0 m. x(2x - 7)(3x - 5) = 0

r - 3 = 0 of r - 9 = 0 x = 0 of 2x - 7 = 0 of 3x - 5 = 0

r = 3 of r = 9 x = 0 of 2x = 7 of 3x = 5

x = 0 of x = 3,5 of x = 1,67

g. 3p(2p + 8) = 0 n. 7t(t2 - 9)(2t + 5) = 0

3p = 0 of 2p + 8 = 0 7t = 0 of t2 - 9 = 0 of 2t + 5 = 0

p = 0 of 2p = -8 t = 0 of t2 = 9 of 2t = -5

p = 0 of p = -4 t = 0 of t = 3 of t = -3 of t = -2,5

8.

a. (x + 7)(x - 3) = 0 h. (5r - 35)(r - 8) = 0 x + 7 = 0 of x - 3 = 0 5r - 35 = 0 of r - 8 = 0

x = -7 of x = 3 5r = 35 of r = 8

r = 7 of r = 8

b. (m - 5)(m + 14) = 0 i. (4 - q)(q + 1,2) = 0

m - 5 = 0 of m + 14 = 0 4 - q = 0 of q + 1,2 = 0

m = 5 of m = -14 q = 4 of q = -1,2

c. (a - 6)(a + 12) = 0 j. 4w(7w + 11) = 0

a - 6 = 0 of a + 12 = 0 4w = 0 of 7w + 11 = 0

a = 6 of a = -12 w = 0 of 7w = -11

w = 0 of w = -1,57

d. s(s - 11) = 0 k. g(g3 + 125) = 0

s = 0 of s - 11 = 0 g = 0 of g3 + 125 = 0

s = 0 of s = 11 g = 0 of g3 = -125

g = 0 of g = -5

e. (n - 1)(n + 2) = 0 l. (k + 9)(4k - 9) = 0

n - 1 = 0 of n + 2 = 0 k + 9 = 0 of 4k - 9 = 0

n = 1 of n = -2 k = -9 of 4k = 9

k = -9 of k = 2,25

f. (r - 2)(r - 11) = 0 m. x(3x - 11)(4x - 11) = 0

r - 2 = 0 of r - 11 = 0 x = 0 of 3x - 11 = 0 of 4x - 11 = 0

r = 2 of r = 11 x = 0 of 3x = 11 of 4x = 11

x = 0 of x = 3,67 of x = 2,75

g. 7p(3p + 18) = 0 n. 25t(t2 - 25)(2t + 25) = 0

7p = 0 of 3p + 18 = 0 25t = 0 of t2 - 25 = 0 of 2t + 25 = 0

p = 0 of 3p = -18 t = 0 of t2 = 25 of 2t = -25

p = 0 of p = -6 t = 0 of t = 5 of t = -5 of t = -12,5

9.

a. x2 + 6x = 0 e. 5x2 - 20x = 0 x(x + 6) = 0 5x(x - 4) = 0

x = 0 of x + 6 = 0 5x = 0 of x - 4 = 0

x = 0 of x = -6 x = 0 of x = 4

b. 6g - 10g2 = 0 f. 4h2 - 22h = 0

2g(3 - 5g) = 0 2h(2h - 11) = 0

2g = 0 of 3 - 5g = 0 2h = 0 of 2h - 11 = 0

g = 0 of -5g = -3 h = 0 of 2h = 11

g = 0 of g = 0,6 h = 0 of h = 5,5

c. 3n2 + 27n = 0 g. 3r - 9r2 = 0

3n(n + 9) = 0 3r (1 - 3r) = 0

3n = 0 of n + 9 = 0 3r = 0 of 1 - 3r = 0

n = 0 of n = -9 r = 0 of -3r = -1

r = 0 of r = 0,33

d. -t2 - 8t = 0 h. -5y2 + 45y = 0

-t(t + 8) = 0 5y(-y + 9) = 0

-t = 0 of t + 8 = 0 5y = 0 of -y + 9 = 0

t = 0 of t = -8 y = 0 of y = 9

10.

a. x4 + 9x3 = 0 e. x5 - 36x3 = 0 x3(x + 9) = 0 x3(x2 - 36) = 0

x3 = 0 of x + 9 = 0 x3 = 0 of x2 - 36 = 0

x = 0 of x = -9 x = 0 of x2 = 36

x = 0 of x = 6 of x = -6

b. 8g2 - 20g3 = 0 f. 6h9 - 48h6 = 0

4g2(2 - 5g) = 0 6h6(h3 - 8) = 0

4g2 = 0 of 2 - 5g = 0 h6 = 0 of h3 - 8 = 0

g2 = 0 of -5g = -2 h = 0 of h3 = 8

g = 0 of g = 0,4 h = 0 of h = 2

c. 5n3 + 35n2 = 0 g. 2r4 - 12r5 = 0

5n2(n + 7) = 0 2r4(1 - 6r) = 0

5n2 = 0 of n + 7 = 0 2r4 = 0 of 1 - 6r = 0

n2 = 0 of n = -7 r4 = 0 of -6r = -1

n = 0 of n = -7 r = 0 of r = 0,17

d. -t4 - 11t3 = 0 h. -7y4 + 56y3 = 0

-t3(t + 11) = 0 7y3(-y + 8) = 0

-t3 = 0 of t + 11 = 0 7y3 = 0 of -y + 8 = 0

t3 = 0 of t = -11 y3 = 0 of y = 8

t = 0 of t = -11 y = 0 of y = 8

11.

a. y = (x + 2)(x + 3) e. v = (c + 4)(c + 12) b. r = (d + 4)(d + 7) f. p = (q + 6)(q - 2)

c. n = (t - 15)(t - 4) g. e = (w - 5)(w - 3)

d. h = (a + 4)(a + 8) h. s = (h - 8)(h + 7)

12.

a. y = (x + 4)(x + 5) e. v = (c + 3)(c + 20) b. r = (d + 2)(d + 16) f. p = (q - 7)(q + 10)

c. n = (t - 6)(t - 9) g. e = (w - 3)(w - 7)

d. h = (a + 5)(a + 7) h. s = (h - 9)(h + 8)

13.

a. a2 + 7a + 6 = 0 e. x2 + 6x - 27 = 0 (a + 6)(a + 1) = 0 (x - 3)(x + 9) = 0

a + 6 = 0 of a + 1 = 0 x - 3 = 0 of x + 9 = 0

a = -6 of a = -1 x = 3 of x = -9

b. b2 - 2b - 15 = 0 f. k2 - k - 42 = 0

(b - 5)(b + 3) = 0 (k - 7)(k + 6) = 0

b - 5 = 0 of b + 3 = 0 k - 7 = 0 of k + 6 = 0

b = 5 of b = -3 k = 7 of k = -6

c. r2 + 12r + 32 = 0 g. q2 - 3q - 18 = 0

(r + 4)(r + 8) = 0 (q - 6)(q + 3) = 0

r + 4 = 0 of r + 8 = 0 q - 6 = 0 of q + 3 = 0

r = -4 of r = -8 q = 6 of q = -3

d. w2 + 4w - 12 = 0 h. z2 - 11z + 30 = 0

(w + 6)(w - 2) = 0 (z - 5)(z - 6) = 0

w + 6 = 0 of w - 2 = 0 z - 5 = 0 of z - 6 = 0

w = -6 of w = 2 z = 5 of z = 6

14.

a. 2a2 + 24a + 22 = 0 e. 3x2 + 15x - 108 = 0 a2 + 12a + 11 = 0 x2 + 5x - 36 = 0

(a + 1)(a + 11) = 0 (x - 4)(x + 9) = 0

a + 1 = 0 of a + 11 = 0 x - 4 = 0 of x + 9 = 0

a = -1 of a = -11 x = 4 of x = -9

b. 3b2 - 30b - 72 = 0 f. 2k2 - 2k - 220 = 0

b2 - 10b - 24 = 0 k2 - k - 110 = 0

(b - 12)(b + 2) = 0 (k - 11)(k + 10) = 0

b - 12 = 0 of b + 2 = 0 k - 11 = 0 of k + 10 = 0

b = 12 of b = -2 k = 11 of k = -10

c. 4r2 + 64r + 220 = 0 g. 0,1q2 - 0,3q - 2,8 = 0

r2 + 16r + 55 = 0 q2 - 3q - 28 = 0

(r + 11)(r + 5) = 0 (q - 7)(q + 4) = 0

r + 11 = 0 of r + 5 = 0 q - 7 = 0 of q + 4 = 0

r = -11 of r = -5 q = 7 of q = -4

d. 0,5w2 + 3w - 8 = 0 h. 1,5z2 - 18z + 52,5 = 0

w2 + 6w - 16 = 0 z2 - 12z + 35 = 0

(w + 8)(w - 2) = 0 (z - 5)(z - 7) = 0

w + 8 = 0 of w - 2 = 0 z - 5 = 0 of z - 7 = 0

w = -8 of w = 2 z = 5 of z = 7

15.

a. a2 + 3a = 40 e. x2 - 15x = 16 a2 + 3a - 40 = 0 x2 - 15x - 16 = 0

(a + 8)(a - 5) = 0 (x - 16)(x + 1) = 0

a + 8 = 0 of a - 5 = 0 x - 16 = 0 of x + 1 = 0

a = -8 of a = 5 x = 16 of x = -1

b. x2 + 8 = 6x f. a2 + 9 = 10a

x2 - 6x + 8 = 0 a2 - 10a + 9 = 0

(x - 4)(x - 2) = 0 (a - 9)(a - 1) = 0

x - 4 = 0 of x - 2 = 0 a - 9 = 0 of a - 1 = 0

x = 4 of x = 2 a = 9 0f a = 1

c. p2 - 4p = 77 g. a2 - 13a = 30

p2 - 4p - 77 = 0 a2 - 13a - 30 = 0

(p - 11)(p + 7) = 0 (a - 15)(a + 2) = 0

p - 11 = 0 of p + 7 = 0 a - 15 = 0 of a + 2 = 0

p = 11 of p = -7 a = 15 of a = -2

d. u2 -11u = 12 h. c2 = -15c

u2 - 11u - 12 = 0 c2 + 15c = 0

(u - 12)(u + 1) = 0 c(c + 15) = 0

u - 12 = 0 of u + 1 = 0 c = 0 of c + 15 = 0

u = 12 of u = -1 c = 0 of c = -15

16.

a. a2 + 13a = 48 e. x2 - 6x = 16 a2 + 13a - 48 = 0 x2 - 6x - 16 = 0

(a + 16)(a - 3) = 0 (x - 8)(x + 2) = 0

a + 16 = 0 of a - 3 = 0 x - 8 = 0 of x + 2 = 0

a = -16 of a = 3 x = 8 of x = -2

b. x2 + 10 = 7x f. a2 + 100 = 29a

x2 - 7x + 10 = 0 a2 - 29a + 100 = 0

(x - 2)(x - 5) = 0 (a - 25)(a - 4) = 0

x - 2 = 0 of x - 5 = 0 a - 25 = 0 of a - 4 = 0

x = 2 of x = 5 a = 25 of a = 4

c. p2 - 18p = 88 g. a2 - 11a = 42

p2 - 18p - 88 = 0 a2 - 11a - 42 = 0

(p - 22)(p + 4) = 0 (a - 14)(a + 3) = 0

p - 22 = 0 of p + 4 = 0 a - 14 = 0 of a + 3 = 0

p = 22 of p = -4 a = 14 of a = -3

d. u2 - 15u = 34 h. c2 = 8c

u2 - 15 u - 34 = 0 c2 - 8c = 0

(u - 17)(u + 2) = 0 c(c - 8) = 0

u - 17 = 0 of u + 2 = 0 c = 0 of c - 8 = 0

u = 17 of u = -2 c = 0 of c = 8

17.

a. 8p(5p - 12) = 0 e. z - 4z = 5 8p = 0 of 5p - 12 = 0 z2 - 4z - 5 = 0

p = 0 of 5p = 12 (z - 5)(z + 1) = 0

p = 0 of p = 2,4 z - 5 = 0 of z + 1 = 0

z = 5 of z = -1

b. 3r2 = 18r f. x2 - 8 = -7x

3r2 - 18 r = 0 x2 + 7x - 8 = 0

3r(r - 6) = 0 (x + 8)(x - 1) = 0

3r = 0 of r - 6 = 0 x + 8 = 0 of x - 1 = 0

r = 0 of r = 6 x = -8 of x = 1

c. -d2 + 4d = 0 g. (w + 4)(3w + 4) = 0

d(-d + 4) = 0 w + 4 = 0 of 3w + 4 = 0

d = 0 of -d + 4 = 0 w = -4 of 3w = -4

d = 0 of d = 4 w = -4 of w = -1,33

d. y2 + 3y - 54 = 0 h. w(7w - 4) = 0

(y + 9)(y - 6) = 0 w = 0 of 7w - 4 = 0

y + 9 = 0 of y - 6 = 0 w = 0 of 7w = 4

y = -9 of y = 6 w = 0 of w = 0,57

18.

a. 7p(4p - 14) = 0 e. z2 - 6z = 7 7p = 0 of 4p - 14 = 0 z2 - 6z - 7 = 0

p = 0 of 4p = 14 (z - 7)(z + 1) = 0

p = 0 of p = 3,5 z - 7 = 0 of z + 1 = 0

z = 7 of z = -1

b. 4r2 = 22r f. x2 + 15 = -16x

4r2 - 22r = 0 x2 + 16x + 15 = 0

2r(2r - 11) = 0 (x + 15)(x + 1) = 0

2r = 0 of 2r - 11 = 0 x + 15 = 0 of x + 1 = 0

r = 0 of 2r = 11 x = -15 of x = -1

r = 0 of r = 5,5

c. -d2 + 7d = 0 g. (w + 6)(5w + 12) = 0

d(-d + 7) = 0 w + 6 = 0 of 5w + 12 = 0

d = 0 of -d + 7 = 0 w = -6 of 5w = -12

d = 0 of d = 7 w = -6 0f w = -2,4

d. y2 + 2y - 99 = 0 h. w(9w - 5) = 0

(y + 11)(y - 9) = 0 w = 0 of 9w - 5 = 0

y + 11 = 0 of y - 9 = 0 w = 0 of 9w = 5

y = -11 of y = 9 w = 0 of w = 0,56

19.

a. 12k = 3k2 e. x2 - 8x - 33 = 0 -3k2 + 12 k = 0 (x - 11)(x + 3) = 0

3k(-k + 4) = 0 x - 11 = 0 of x + 3 = 0

3k = 0 of -k + 4 = 0 x = 11 of x = -3

k = 0 of k = 4

b. s2 - s = 12 f. (5r - 7)(8r - 15)= 0

s2 - s - 12 = 0 5r - 7 = 0 of 8r - 15 = 0

(s - 4)(s + 3) = 0 5r = 7 of 8r = 15

s - 4 = 0 of s + 3 = 0 r = 1,4 of r = 1,88

s = 4 of s = -3

c. p2 + 34 = -19p g. 3x2 - 5x - 14 = 2x2

p2 + 19p + 34 = 0 x2 -5x - 14 = 0

(p + 17)(p + 2) = 0 (x - 7)(x + 2) = 0

p + 17 = 0 of p + 2 = 0 x - 7 = 0 of x + 2 = 0

p = -17 of p = -2 x = 7 of x = -2

d. q2 + 68q = 72q h. -4p2 + 5p - 18 = -5p2 + p + 27

q2 - 4q = 0 p2 + 5p - 18 = p + 27

q(q - 4) = 0 p2 + 4p - 18 = 27

q = 0 of q - 4 = 0 p2 + 4p - 45 = 0

q = 0 of q = 4 (p + 9)(p - 5) = 0

p + 9 = 0 of p - 5 = 0

p = -9 of p = 5

20.

a. 16k = 8k2 e. x2 - 20x - 44 = 0 -8k2 + 16k = 0 (x - 22)(x + 2) = 0

8k(-k + 2) = 0 x - 22 = 0 of x + 2 = 0

8k = 0 of -k + 2 = 0 x = 22 of x = -2

k = 0 of k = 2

b. s2 - s = 2 f. (4r - 9)(3r - 17)= 0

s2 - s - 2 = 0 4r - 9 = 0 of 3r - 17 = 0

(s - 2)(s + 1) = 0 4r = 9 of 3r = 17

s - 2 = 0 of s + 1 = 0 r = 2,25 of r = 5,67

s = 2 of s = -1

c. p2 + 54 = -21p g. 7x2 - 2x - 24 = 6x2

p2 + 21p + 54 = 0 x2 - 2x - 24 = 0

(p + 18)(p + 3) = 0 (x - 6)(x + 4) = 0

p + 18 = 0 of p + 3 = 0 x - 6 = 0 of x + 4 = 0

p = -18 of p = -3 x = 6 of x = -4

d. q2 + 5q = 11q h. -8p2 + 6p - 18 = -9p2 + 3p + 70

q2 - 6q = 0 p2 + 6p - 18 = 3p + 70

q(q - 6) = 0 p2 + 3p - 18 = 70

q = 0 of q - 6 = 0 p2 + 3p - 88 = 0

q = 0 of q = 6 (p + 11)(p - 8) = 0

p + 11 = 0 of p - 8 = 0

p = -11 of p = 8

21.

a. b. Voor de snijpunten met de x-as geldt: y = 0 x2 - 2x - 8 = 0 (x - 4)(x + 2) = 0 x - 4 = 0 of x + 2 = 0 x = 4 of x = -2 De snijpunten zijn (4, 0) en (-2, 0) c. x2 - 2x - 8 = -5 x2 - 2x - 3 = 0 (x - 3)(x + 1) = 0 x - 3 = 0 of x + 1 = 0 x = 3 of x = -1 de snijpunten met de lijn y = -5 zijn (3,-5) en (-1,-5)

d. x2 - 2x - 8 = 7 x2 - 2x - 15 = 0 (x - 5)(x + 3) = 0 x - 5 = 0 of x + 3 = 0 x = 5 of x = -3 de snijpunten met de lijn y = 7 zijn (5,7) en (-3,7) e. x2 - 2x - 8 = 5x x2 - 7x - 8 = 0 (x - 8)(x + 1) = 0 x - 8 = 0 of x + 1 = 0 x = 8 of x = -1 y = 5. 8 = 40 of y = 5.-1 = -5 de snijpunten met de lijn y = 5x zijn (8,40) en (-1,-5)

22.

a. b. Voor de snijpunten met de x-as geldt: y = 0 x2 - 6x = 0 x(x - 6) = 0 x = 0 of x - 6 = 0 x = 0 of x = 6 De snijpunten zijn (0,0) en (6, 0)

c. x2 - 6x = -8 x2 - 6x + 8 = 0 (x - 4)(x - 2) = 0 x - 4 = 0 of x - 2 = 0 x = 4 of x = 2 de snijpunten met de lijn y = -8 zijn (4,-8) en (2,-8) d. x2 - 6x = 16 x2 - 6x - 16 = 0 (x - 8)(x + 2) = 0 x - 8 = 0 of x + 2 = 0 x = 8 of x = -2 de snijpunten met de lijn y = 16 zijn (8,16) en (-2,16) e. x2 - 6x = -2x x2 - 4x = 0 x(x - 4) = 0 x = 0 of x - 4 = 0 x = 0 of x = 4 y = -2. 0 = 0 of y = -2.4 = -8 de snijpunten met de lijn y = -2x zijn (0,0) en (4,-8)

23. 1,5a - 1/40a2 = 0 60a - a2 = 0 a(60 - a) = 0 a = 0 of 60 - a = 0 a = 0 of a = 60 De brug is dus 60 meter breed. b. 1,5a - 1/40a2 = 12,5 60a - a2 = 500 0 = a2 - 60a + 500 (a - 10)(a - 50) = 0 a - 10 = 0 of a - 50 = 0 a = 10 of a = 50 c. Het hoogste punt ligt in het midden van de brug bij a = 30. De hoogte is dan 1,5 . 30 + 1/40 . 302 = 22,5 meter

24. 2a - 1/50a2 = 0 100a - a2 = 0 a(100 - a) = 0 a = 0 of 100 - a = 0 a = 0 of a = 100 De brug is dus 100 meter breed. b. 2a - 1/50a2 = 32 100a - a2 = 1600 0 = a2 - 100a + 1600 (a - 80)(a - 20) = 0 a - 80 = 0 of a - 20 = 0 a = 80 of a = 20 c. Het hoogste punt ligt in het midden van de brug bij a = 50. De hoogte is dan 2 . 50 + 1/50 . 502 = 50 meter

©A. Gottemaker