Sample Project: Modeling Quadratic Functions in Real-Life
The Pont d’Arc
(Photo source: EzineMark.com)
The Pont d’Arc is located in the south of France near the village of Vallon-Pont-
d’Arc. It is the largest natural arch in all of Europe. The arch straddles the
Ardèche River, named for the person who discovered it. This arch was created
over thousands of years by the Ardèche, which eventually broke its way through
The Arch is home to many caves, including Chauvet Cave, which was
discovered in 1994. The cave was named after Jean-Marie Chauvet, one of the
speleologists to initially explore the cave. The cave is home to some of the
earliest known prehistoric cave paintings dating back 30,000 years.
Accounts of the dimensions of the arch differ. EzineMark.com, an online
directory, claims the arch stands 45 meters high and 60 meters wide. A travel
guide, Experienceardeche.com claims the arch stands 66 meters high and has
a span of 34 meters. According to Wikipedia.org the arch is 40 meters high and
60 meters wide.
Since the bridge is clearly wider than it is tall, I chose the Wikipedia dimensions to
create an algebraic model for Pont d’Arc.
Using the 60-meter width of the arch, I let the x-intercepts correspond to 0 and
The vertex of the parabolic model would occur halfway between the intercepts,
which gives us x = 30. We know the height of the arch is 40 meters, so that
corresponds to the y-value of the vertex. The vertex of the parabola is (30, 40).
The value of a was determined by substituting the given values into the
Intercept form of the quadratic equation and solving for the coefficient.
Intercept Form: or
Vertex Form: or
Standard Form: or