Did you get for b) ==> -1/4 < k < 3
for c) draw a parabola, since we know the equation involves k^2
(a parabola is the U curve).
now it mentions to state the coordinates of any intersections with the coordinate axes. Before, it told us that the equation f(x)=0 has no real roots, this means it does not cross the x-axis.
The minimum point can be worked out from the equation (x+p)^2 + q.
I got: p=2k q=(-4k^2 + 3 + 11k)
then it says k=1
so p=2 and q=(-4 + 3 + 11) = 14-4 = 10
p=2 q=10
now then we have (x+2)^2 + 10
so our minimum point is (-2,10)
it is -2 not +2 since, the equation takes the form: (x-a)^2 + b
but in this case "a" must be negative since we have ( x+2) ===> i.e. (x-(-2)) = (x+2)
so you draw a U curve with the minimum point at (-2,10)
Now it crosses the y axis when x=0 ===> so put x=0 into this equation and we get:
(x+2)^2 + 10
(0+2)^2 + 10 = 14
so it crosses the y-axis at (0,14)
I hope this helps!