就快模擬考試 ,但唔識做(4)

(a)
When contracts by k times,
y = k(x^2 - 4x - 12) where 0 < k < 1......(1) [ Note : k > 1 will be enlargement]
When up shift by (1 - 12k)/4k units,
y = g(x) = k(x^2 - 4x - 12) + (1 - 12k)/4k = kx^2 - 4kx - 12k + (1 - 12k)/4k
(b)
For g(x) to be always above the x - axis, delta < 0
(-4k)^2 - (4)(k)[ - 12k + (1 - 12k)/4k] < 0
16k^2 + 48k^2 - 1 + 12k < 0
64k^2 + 12k - 1 < 0
(4k + 1)(16k - 1) < 0
- 1/4 < k < 1/16...............(2)
From (1) and (2)
0 < k < 1/16
or 0 < k < 0.0625