1. Resolve the initial velocity

If the particle is projected with speed $u$ at an angle $\phi$ from the vertical, then its vertical component is

$u_y = u\cos\phi$

and horizontal component is

$u_x = u\sin\phi.$

2. Use the formula for maximum height

For projectile motion, maximum height is determined only by the initial vertical component:

$h_m = \frac{u_y^2}{2g}.$

Substituting $u_y = u\cos\phi$,

$h_m = \frac{(u\cos\phi)^2}{2g}$

$h_m = \frac{u^2}{2g}\cos^2\phi.$

3. Interpretation as a function of $\phi$

Thus,

$h_m(\phi) = \frac{u^2}{2g}\cos^2\phi.$

So the graph/function is proportional to $\cos^2\phi$.

4. Match with the correct option

The correct option is the one representing

$h_m \propto \cos^2\phi.$

Hence, the answer should be Option D.

5. Comparison with stored answer

Stored correct answer = D.

This matches our derived answer.