Okay, I'm going to try this
:
a) x^2 + 4kx = (x + 2k)^2 - 4k^2 therefore x^2 + 4kx + (3 + 11k) = (x + 2k)^2 - 4k^2 + 3 + 11k
therefore p = 2k and q = - 4k^2 + 3 + 11k
b) Since f(x) = 0 has no real roots, b^2 - 4ac < 0
a = 1, b = 4k and c = (3 + 11k)
therefore (4k)^2 - 4(1)(3 + 11k) < 0
therefore 16k^2 - 44k - 12 < 0
then divide by 4, so therefore 4k^2 - 11k - 3 < 0
therefore factorise so (4k + 1)(k - 3) < 0
therefore k = -1/4 or k = 3
therefore -1/4 < k < 3
c) k = 1 therefore using (x + 2k)^2 - 4k^2 + 3 + 11k, you know that y = (x + 2)^2 - 4 + 3 + 11 = (x + 2)^2 + 10
when x = 0, y = 14 therefore the curve cuts the y-axis at (0,14)
the curve will not cut the x-axis because f(x) = 0 has no real roots
the lowest point of the curve will be (-2,10)
I hope this helps
