How to do it...

Thanks to our previous hard work, this recipe is a real piece of cake:

1. Create the GetFireDirection function:

public static Vector3 GetFireDirection (Vector3 startPos, Vector3 endPos, float speed) 
{ 
    // body 
}

2. Solve the corresponding quadratic equation:

Vector3 direction = Vector3.zero; 
Vector3 delta = endPos - startPos; 
float a = Vector3.Dot(Physics.gravity, Physics.gravity); 
float b = -4 * (Vector3.Dot(Physics.gravity, delta) + speed * speed); 
float c = 4 * Vector3.Dot(delta, delta); 
if (4 * a * c > b * b) 
    return direction; 
float time0 = Mathf.Sqrt((-b + Mathf.Sqrt(b * b - 4 * a * c)) / (2*a)); 
float time1 = Mathf.Sqrt((-b - Mathf.Sqrt(b * b - 4 * a * c)) / (2*a)); 

3. If shooting the projectile is feasible given the parameters, return a non-zero direction vector:

float time; 
if (time0 < 0.0f) 
{ 
    if (time1 < 0) 
        return direction; 
    time = time1; 
} 
else 
{ 
    if (time1 < 0) 
        time = time0; 
    else 
        time = Mathf.Min(time0, time1); 
} 
direction = 2 * delta - Physics.gravity * (time * time); 
direction = direction / (2 * speed * time); 
return direction;