中4 Qadratic equations

(26) (i) y = -2x^2 - 12x + k
Since the curve touches the x-axis, 0 = -2x^2 - 12k + k has double roots
Discriminant = 12^2 - (4)(-2)(k) = 0
144 + 8k = 0
k = -18
(ii) y = -2x^2 - 12x - 18
y = -2(x + 3)^2
P is (-3,0)
when x = 0, y = -18
Q is (0, -18)
(b) Area of OPQ = Base x Height / 2 = 3 * 18 / 2 = 27
(27) (a) y = kx^2 + (3 - k/2)x + 6k cut the y-axis at C(0,3)
=> 3 = 0 + 0 + 6k
=> k = 1/2
(b) y = x^2/2 + 11x/4 + 3
when y = 0,
x^2/2 + 11x/4 + 3 = 0
2x^2 + 11x + 12 = 0
(2x + 3)(x + 4) = 0
x = -3/2 or x = -4
OA + OB = 3/2 + 4 = 11/2