Chapter 5 Project
Integrated Math 2
You need to complete 2 of the 4 problems in Section A and 1 of the 2 problems in Section B. They are
due by 5:00 pm on Friday, December 9. If turned in after that time but before 2:00 pm on Monday,
December 12, you can receive credit, but the maximum number of points you can score is 3. Each
question will be graded on a 4 point scale if they are turned in by Friday, December 9, at 5:00 pm.
4 points – Everything is perfect, including work and units
3 points – Answer is mostly correct and work is mostly correct
2 points – Work is partially correct, including a complete drawing
1 point – Attempt is made with at least a partial drawing
0 points – No attempt is made or nothing is turned in
You may ask any questions you have, and anything that helps you toward the solution will be answered.
Section A
Question A-1: CPM 5-59(a) - Ernie is going to install a square hot tub in his backyard. He plans to add a
3-foot-wide deck on two adjacent sides of the hot tub. If Ernie’s backyard (which is also a square) has
169 square feet of space, what is the largest hot tub he can order?
Question A-2: CPM 5-59(b) - Gabi is creating a decorative rock garden that will cover 12 square feet of
her back yard, including its frame. She plans to build a 6-inch wide wood frame around the rock garden
to keep the rocks in place. If the framed rock garden is square, how much area will Gabi need to cover
with decorative rocks?
Question A-3: CPM 5-108 - Gabi is working on another backyard project. She is building a fence to keep
deer out of her garden. One side of her garden is against a wall, so she only needs to build three sides of
the fence. She has 100 feet of fencing. If she needs to enclose a 600 square foot area, what should the
length and width of her fence be?
Question A-4: CPM 5-109 - Karen drives straight south on Interstate 405 from the Santa Monica Freeway
interchange going 10 miles per hour faster than Melinda, who leaves the same interchange at the same
time going straight east on Interstate 10. After one hour they are 108 miles apart, measured by a
straight line drawn between them. How fast is each driver going? State any assumptions you make.
Chapter 5 Project
Integrated Math 2
Section B
Question B-1: CPM 5-110 - Arches like the Saint Louis Gateway Arch
(pictured at right) are not parabolas. But sometimes arches are modeled
using a parabola so that predictions are possible.
Ramon’s company has been hired to set up a concert stage approximately
15 feet from one base of the arch. One of the bands that will be performing
uses a 30-foot tall guitar as one of its props, and Ramon is worried that it
will not fit under the arch.
He adds coordinate axes to the drawing above to model the Gateway Arch, where both x and y
represent distance in feet and the origin is the point on the ground directly below the arch’s apex (its
highest point). He knows that the arch is 630 feet wide and 630 feet tall. Use the problems below to
help Ramon decide if he should be worried.
a) Help Ramon write a function to model the height of the arch relative to the horizontal position
from the center (the y value at the vertex should be 630 feet. Use www.desmos.com to verify
that your model is correct.
b) How tall is the arch 15 feet from its base? Should Ramon be worried?
c) What is a useful domain (x values) for this model of the St. Louis Gateway Arch?
Question B-2: CPM 5-111 - Moe is playing with a yo-yo. He throws the yo-yo down and then pulls it back
up. The motion of the yo-yo can be roughly modeled by the equation 𝑦 = 2𝑥 2 − 4.8𝑥, where x
represents the number of seconds since the yo-yo left Moe’s hand, and y represents the vertical height
in feet of the yo-yo with respect to Moe’s hand. Note that when the yo-yo is in Moe’s hand, y = 0, and
when the yo-yo is below his hand, y is negative.
a) How long is Moe’s yo-yo out of his hand? In other words, what is the difference between the
two zeros of the equation?
b) Once the yo-yo leaves Moe’s hand, how long does it take for the yo-yo to turn around, that is, to
start its return to his hand? Use what you know about parabolas to help you.
c) How long is the yo-yo’s string? Assume that all the string has been let out when the yo-yo
changes direction.
d) Sketch a graph representing the motion of Moe’s yo-yo. On the sketch, label the important
points: when the yo-yo is in Moe’s hand and when it changes direction.