$h = 0,0625 \cdot 40^{2} = 100$ m

als $x = 0$ , $h = 0,0625 \cdot 0^{2} = 0$ m
als $x = 10$ , $h = 0,0625 \cdot 10^{2} = 6,25$ m
als $x = 20$ , $h = 0,0625 \cdot 20^{2} = 25$ m
als $x = 30$ , $h = 0,0625 \cdot 30^{2} = 56,25$ m
als $x = 40$ , $h = 0,0625 \cdot 40^{2} = 100$ m

als $x = 35$ , $h = 0,0625 \cdot 35^{2} = 76,5625$ m
De hoogte boven de Wupper is dan $100 - 76,5625 = 23,4375$ m.

Nulpunten

$x^{2} - 6 x = 0$
$x (x - 6) = 0$
$x = 0$ of $x = 6$
Dus de nulpunten zijn 0 en 6.

symmetrieas: $x = \frac{0 + 6}{2} = 3$

$y = 3^{2} - 6 \cdot 3 = ‐ 9$ , Top $(3, ‐ 9)$

Zie antwoord opgave e.

$y = x^{2} - 6 x + 9 = {(x - 3)}^{2}$

$x^{2} + 8 x = 0$
$x (x + 8) = 0$
$x = 0$ of $x = ‐ 8$
Dus de nulpunten zijn 0 en $‐ 8$ .

symmetrieas: $x = \frac{‐ 8 + 0}{2} = ‐ 4$

$y = {(‐ 4)}^{2} + 8 \cdot ‐ 4 = ‐ 16$ , Top $(‐ 4, ‐ 16)$

$y = x^{2} + 8 x + 16 = {(x + 4)}^{2}$

$‐ x^{2} - 2 x = 0$
$‐ x (x + 2) = 0$
$x = 0$ of $x = ‐ 2$
Dus de nulpunten zijn 0 en $‐ 2$ .

symmetrieas: $x = \frac{‐ 2 + 0}{2} = ‐ 1$

$y = ‐ {(‐ 1)}^{2} - 2 \cdot ‐ 1 = ‐ 1 + 2 = 1$ , Top $(‐ 1,1)$

$‐ 1$

$\frac{18}{45} = \frac{12}{y}$
$18 y = 540$
$y = 30$
$O = 12 \cdot (45 - 30) = 180$

$\frac{18}{45} = \frac{x}{y}$
$18 y = 45 x$
$y = 2 \frac{1}{2} x$

Breedte van de rechthoek is $45 - y = 45 - 2 \frac{1}{2} x$
$O = x \cdot (45 - 2 \frac{1}{2} x) = 45 x - 2 \frac{1}{2} x^{2}$

$45 x - 2 \frac{1}{2} x^{2} = 0$
$2 \frac{1}{2} x (18 - x) = 0$
$x = 0$ of $x = 18$
De oppervlakte is maximaal als $x = \frac{18 + 0}{2} = 9$ .

De oppervlakte is dan $45 \cdot 9 - 2 \frac{1}{2} \cdot 9^{2} = 202 \frac{1}{2}$ .

Snijpunt met de y-as

snijpunt $y$ -as $\Rightarrow x = 0$
$y = 0^{2} - 2 \cdot 0 + 4 = 4$
$(0,4)$

$x^{2} - 2 x + 4 = 4$
$x^{2} - 2 x = 0$
$x (x - 2) = 0$
$x = 0$ of $x = 2$

symmetrieas: $x = \frac{0 + 2}{2} = 1$

$y = 1^{2} - 2 \cdot 1 + 4 = 3$ , Top $(1,3)$

$y = ‐ 2 \cdot 0^{2} + 4 \cdot 0 + 2 = 2$
Snijpunt $y$ -as $(0,2)$

$‐ 2 x^{2} + 4 x + 2 = 2$
$‐ 2 x^{2} + 4 x = 0$
$‐ 2 x (x - 2) = 0$
$x = 0$ of $x = 2$

symmetrieas: $x = \frac{0 + 2}{2} = 1$

$y = ‐ 2 \cdot 1^{2} + 4 \cdot 1 + 2 = 4$
Top $(1,4)$

$y = x^{2} - 2 x$
Nulpunten:
$x^{2} - 2 x = 0$
$x (x - 2) = 0$
$x = 0$ of $x = 2$

Snijpunt $y$ -as:
$y = 0^{2} + 2 \cdot 0 = 0$
$(0,0)$

Symmetrieas:
$x = \frac{0 + 2}{2} = 1$
$y = 1^{2} - 2 \cdot 1 = ‐ 1$
Top $(1, ‐ 1)$

$y = ‐ x^{2} + 5 x - 2$

Snijpunt $y$ -as:
$y = ‐ 0^{2} + 5 \cdot 0 - 2 = ‐ 2$
$(0, ‐ 2)$

$‐ x^{2} + 5 x - 2 = ‐ 2$
$‐ x^{2} + 5 x = 0$
$‐ x (x - 5) = 0$
$x = 0$ of $x = 5$

Symmetrieas:
$x = \frac{0 + 5}{2} = 2 \frac{1}{2}$
$y = ‐ {(2 \frac{1}{2})}^{2} + 5 \cdot 2 \frac{1}{2} - 2 = 4 \frac{1}{4}$
Top $(2 \frac{1}{2},4 \frac{1}{4})$

$y = (x + 2) (x - 8)$
Nulpunten:
$(x + 2) (x - 8) = 0$
$x = ‐ 2$ of $x = 8$

Snijpunt $y$ -as:
$y = (0 + 2) (0 - 8) = ‐ 16$
$(0, ‐ 16)$

Symmetrieas:
$x = \frac{‐ 2 + 8}{2} = 3$
$y = (3 + 2) (3 - 8) = ‐ 25$
Top $(3, ‐ 25)$

$y = 2 x^{2} - 3 x + 1$

Snijpunt $y$ -as:
$y = 2 \cdot 0^{2} - 3 \cdot 0 + 1 = 1$
$(0,1)$

$2 x^{2} - 3 x + 1 = 1$
$2 x^{2} - 3 x = 0$
$2 x (x - 1 \frac{1}{2}) = 0$
$x = 0$ of $x = 1 \frac{1}{2}$
Symmetrieas:
$x = \frac{0 + 1 \frac{1}{2}}{2} = \frac{3}{4}$
$y = 2 \cdot {(\frac{3}{4})}^{2} - 3 \cdot \frac{3}{4} + 1 = ‐ \frac{1}{8}$
Top $(\frac{3}{4}, ‐ \frac{1}{8})$

$y = ‐ 3 x^{2} - 9 x + 6$

Snijpunt $y$ -as:
$y = ‐ 3 \cdot 0^{2} - 9 \cdot 0 + 6 = 6$
$(0,6)$

$‐ 3 x^{2} - 9 x + 6 = 6$
$‐ 3 x^{2} - 9 x = 0$
$x^{2} + 3 x = 0$
$x (x + 3) = 0$
$x = 0$ of $x = ‐ 3$

Symmetrieas:
$x = \frac{0 + ‐ 3}{2} = ‐ 1 \frac{1}{2}$
$y = ‐ 3 \cdot {(‐ 1 \frac{1}{2})}^{2} - 9 \cdot ‐ 1 \frac{1}{2} + 6 = 12 \frac{3}{4}$
Top $(‐ 1 \frac{1}{2},12 \frac{3}{4})$