Problem of the Week: Parabulous!
Editor’s Note: The Department of Mathematics at Gettysburg College hosts a problem of the week challenge to determine each semester’s Paul Mugabi problem-solving award recipient(s). Each week’s entries are scored by a faculty judge, and winner(s) from each week will receive a Problem Of the Week (P.O.W.) button. The Gettysburgian is not involved in or responsible for accepting or evaluating students’ submissions to this contest.
THE RULES:
The contest is open to all Gettysburg College students. Up to three people may work together on a submission. Make sure your name is on your submission and that any sources are properly cited. Send solutions to bkennedy@gettysburg.edu. This problem was posted on Sunday, October 24 and solutions are due on Friday, October 29 by 5:00 p.m.
THE PROBLEM:
Suppose that we are looking at the graph of a parabola of the form 
.
We mark three points on the graph: the bottom of the parabola, and the two points on the parabola that are the same height and exactly one unit part.
(Image courtesy of Benjamin Kennedy)
THE QUESTION: What is the area of the triangle determined by these three points?
