(E) it is

A line does not have to be straight

... Here, we are with the example, it's 2 curves that we are speaking about.

The best way here is to draw XY planes.

We have:
o y = ax^2 + b

o y = cx^2 + d

A first thing to know, when we have such form of curves (no t*x involved), a curve is simetrical to the Y-axis, reaching an extremum at x=0.

A second thing is that a and c have a direct impact on the widths of the curves and on the shape of them : "valleys" or "mountains".

Now, let us go in the statments.

Stat1
a=-c.... Implies a similar width but a different shape. The one that is positive represents a valley and so the other that is negatize creates a montain.

All depend on the values of b and d to intersect.

o If b=d, we have a single point of intersection on the Y axis.

o If b > d, we have 2 cases :

- a > c : the 2 curves have no intersection and as the line X Axis as an axis of symetry

- a < c : the 2 curves have 2 intersections (symetrical to the Y axis) and as the line X Axis as an axis of symetry

o If b < d, we have 2 cases :

- a > c : the 2 curves have 2 intersections (symetrical to the Y axis) and as the line X Axis as an axis of symetry

- a < c : the 2 curves have no intersection and as the line X Axis as an axis of symetry

INSUFF.

Stat2
b > d.

This just says that the 2 extremum of the 2 curves are situated one above the other one.

That's not giving informations on:
- the width of the cuvres : 1 valley with a smaller width could be contained in 1 valley with a larger width

- the shapes of the curves: 2 valleys, 1 mountain and 1 valley or 2 mountains

INSUFF.

Both 1 and 2
We are left with the 2 cases as a=-c:

b > d :
- a > c : the 2 curves have no intersection and as the line X Axis as an axis of symetry

- a < c : the 2 curves have 2 intersections (symetrical to the Y axis) and as the line X Axis as an axis of symetry

INSUFF.