Question 139185
a) the graph of the function is a parabola.  since the lead coefficient is negative, the parabola opens downward, meaning the vertex is a maximum of the function.  If you need the calculus solution, the second derivitive is {{{-64/(50)^2}}}, so it is everywhere negative in the domain of the function, hence the extreme point is a maximum.


b) The x-coordinate of the vertex of any parabola in the form {{{f(x)=ax^2+bx+c}}} is given by {{{-b/2a}}}.  So evaluate {{{-1/(2(-32/(50)^2))}}} to find the value of x, i.e. the horizontal distance, at the vertex, or maximum.


c) If the the function represents the height above the water of the projectile for any given horizontal distance, and if that height is zero, then the projectile is impacting the water.  So setting the function equal to zero and solving for x gives you the horizontal distance from the base of the cliff to the point of impact with the water.  Hopefully, the enemy ship is in the same place -- but that is just an old sailor talking.