Two pillars support the archway entrance of a castle. the archway can be modelled by the relation h=-0.025d^2 +d

For this case we have the following function:
 
 To find the distance between the pillars, we must match the equation to zero:
 
 From here, we clear the value of d:
 
 The roots are:
 Root 1:
 
 Root 2:
 
 Thus, the pillars are 40 units away.

 The maximum height, we obtain it by deriving:
 
 We equal zero and clear d:
 
 Then, we substitute the value of d = 20 in the equation for the height:
 
 The maximum height is 10 units of distance

Ugh h h t t u i i vick u