Question has to do with intercept, vertex, and standard form, story problem.

Question

Your class council determined that it's profit from the upcoming homecoming dance is directly related to the ticket price for the dance. Looking at past dances, the council determined that the profit (p) can be modeled by the function p(t)=-12t squared +480t+30, where t represents the price of each ticket. What should be the price of a ticket to the homecoming dance to maximize the council's profit?

Answer 1

Grammatical Note" -- use its (no apostrophe) for possessive; it's is only used as contraction of "it is"

 

p(t) will be a parabola opening downwardly; its vertex is the highest function value.

The t value of the vertex is computed as t = -b/(2a)  where a = 12 & b = 480 in this instance.

 

Then evaluate p at that particular t_vertex point to get maximum profit.