SOLUTION: I need help in writing a word problem involving a quadratic function. And I need to explain it in terms someone not in class could understand it, please. I am in the home stretch o

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Question 730485: I need help in writing a word problem involving a quadratic function. And I need to explain it in terms someone not in class could understand it, please. I am in the home stretch of my class and would really appreciate the help. Thank you
Answer by MathLover1(20855) (Show Source):
You can put this solution on YOUR website!

A function is a quadratic function if where , , and are real numbers and not equal to .
The graph of a quadratic function is a . The most basic aid in graphing a parabola is knowing whether (the graph opens ) or (the graph opens ).
The two simplest quadratic functions are and .
a word problem involving a quadratic function:
An inquiry shows that students will attend a theater play in one week if the ticket price is dollars. Suppose that for every dollars added to the ticket price, fewer students will attend the play.
1. What ticket price will give the for the week?
2. what is the approximate for the week if the theater play spends approximately million dollars to have the play showed for one week?
answer:
1. Let be the number of times $ is added to the ticket price (and fewer students attend).
Revenue for the week is
=
=
=
Thus the greatest revenue is given by the maximum of function . It is a quadratic function with a maximum of where is the value of for which the revenue will be greatest.
To answer the question, calculate the corresponding ticket price by adding $ to the original $.
2.
Since spendings are fixed, maximum profit is obtained when maximum revenue is obtained as above, for .

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