SOLUTION: an arch in the form of an inverted parabola and has a span of 12 feet at the base and a height of 12 feet. determine the vertical clearance of the parabola 4 feet from the vertical

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: an arch in the form of an inverted parabola and has a span of 12 feet at the base and a height of 12 feet. determine the vertical clearance of the parabola 4 feet from the vertical      Log On


   



Question 1086406: an arch in the form of an inverted parabola and has a span of 12 feet at the base and a height of 12 feet. determine the vertical clearance of the parabola 4 feet from the vertical centerline
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
The equation of this parabola is 

p(x) = -%281%2F3%29%2A%28x-6%29%2A%28x%2B6%29

(6 units to the left from the vertical centerline to one root and 6 units to the right to the other root;
 and the vertex is at 12 ft up).


Now, the question asks about p(4), and you can easy calculate it:

p(4) = -%281%2F3%29%2A%284-6%29%2A%284%2B6%29 = %28-1%2F3%29%2A%28-2%29%2A10 =  20%2F3 = 62%2F3 ft.

Answer.   Verical clearance of the parabola  4 feet from the vertical centerline is  62%2F3  ft.