Roller Coaster Design
Worksheet
Graphing Radical Functions, Radical Equations and
Extraneous Roots, Solving Equations Containing
Two Radicals
You are on a team of architects. You are charged with building a scale-model replica of one
section of a new roller coaster before construction gets underway.
Certain reinforcement cables and struts are required to make the roller coaster sturdier. The goal
for this project is for your team to determine where to place these cables or struts. The
mathematical models for these reinforcements are known.
Your team must provide both algebraic and graphical evidence for your conclusions regarding the
location of the cables.
The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the
origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
1. Write the equation that models the height of the roller coaster.
Start by writing the equation of the circle. (Recall that the general form of a circle with the center
at the origin is x2 + y2 = r2. (10 points)
x^2+y^2=30^2 (the radius is 30 ft) x^2+y^2=900
y. Remember the roller coaster is above ground, so you are only
Now solve this equation for
interested in the positive root. (10 points)
y = √(900 - x^2)
2. Graph the model of the roller coaster using the graphing calculator. Take a screenshot of your
graph and paste the image below, or sketch a graph by hand. (5 points)
Copyright© E2020, Inc. 2011
Worksheet
Graphing Radical Functions, Radical Equations and
Extraneous Roots, Solving Equations Containing
Two Radicals
You are on a team of architects. You are charged with building a scale-model replica of one
section of a new roller coaster before construction gets underway.
Certain reinforcement cables and struts are required to make the roller coaster sturdier. The goal
for this project is for your team to determine where to place these cables or struts. The
mathematical models for these reinforcements are known.
Your team must provide both algebraic and graphical evidence for your conclusions regarding the
location of the cables.
The shape of this particular section of the rollercoaster is a half of a circle. Center the circle at the
origin and assume the highest point on this leg of the roller coaster is 30 feet above the ground.
1. Write the equation that models the height of the roller coaster.
Start by writing the equation of the circle. (Recall that the general form of a circle with the center
at the origin is x2 + y2 = r2. (10 points)
x^2+y^2=30^2 (the radius is 30 ft) x^2+y^2=900
y. Remember the roller coaster is above ground, so you are only
Now solve this equation for
interested in the positive root. (10 points)
y = √(900 - x^2)
2. Graph the model of the roller coaster using the graphing calculator. Take a screenshot of your
graph and paste the image below, or sketch a graph by hand. (5 points)
Copyright© E2020, Inc. 2011
