Quadratic Functions Project – Profit Parabolas
One of the many applications of quadratic functions in called the Profit Parabola. The Profit Parabola can
be seen if we investigate the following scenario:
The business manager of a 90 unit apartment building is trying to determine the rent to be charged.
From past experience with similar buildings, when rent is set at $400, all the units are full. For every $20
increase in rent, one additional unit remains vacant. What rent should be charged for maximum total
revenue? What is that maximum total revenue?
To help solve the above scenario, perform an internet search for Profit Parabola or Applications of
Quadratic Functions. List the URL of one of the applications that you find and attach it to the back of this
project url:http://www.mathsisfun.com/algebra/quadratic-equation.html
_________________________________________________________________
Go to http://www.purplemath.com/modules/quadprob3.htm to see the process used for determining
the quadratic function for revenues R(x) as a function of price hikes x on page 3 with the canoe-rental
business problem. Use this process to determine the quadratic function that models the revenues R(x)
as a function of price hikes x in the apartment building scenario above. SHOW ALL YOUR WORK!
Rent
hikes
none
1
2
3
x Rent per
apartment
$400
$420
$440
$460
400+x (20) Number of
rentals
90
90-(1)
90-(2)
90-(3)
90-x Total revenue
400*90=36,000
420*89=37,380
440*88=38,720
460*87=40,020
400+x (20) (90-x) =0 What is the formula for revenues R after x $20 price hikes in the apartment building? Graph the function and attach the graph.
Find the maximum revenue (or income) of the apartment building. What is the rent that coincides with this maximum revenue?
What is the outcome if the rent hike of $20 results in 2 additional vacancies instead of 1? MTH109 Set up a similar scenario, of your own invention, using a business that you are interested in. Write up
the scenario (problem) and the solution process involved. Find the solution to the problem you
invented. Graph the function and attach it. MTH109

Attachments:

• 1492665531-Quadratic Functions Profit Parabola.docx