Math 2
Name: _______________________
2-2 practice
1. The Drop of Doom is a roller coaster at Six Flags Magic Mountain in Valencia,
California. The Drop of Doom drops thrill seekers from record-breaking height. Use the
formula f (t )  16t 2  400 to determine the height of the coaster at several times during
the descent and use the data to determine how long it takes the coaster to reach the
bottom.
a. Complete the table to determine how long it takes Drop of Doom to reach the bottom
of its highest drop:
time t (seconds)
height (feet)
ordered pair
f (t )  16t 2  400
(t, f(t))
0
1
2
3
4
5
b. Graph the ordered pairs to the right.
c.
What is the height of the coaster
before it begins the drop? How do you
know?
d.
After how many seconds does the
Drop of Doom reach the bottom?
How do you know?
2.
a.
Fill in the table for each function.
f(x) = 2 + (x – 1)(– 3)
g(x) = 10 – 16x2
h(x) = x3- 2
b.
Make a conjecture about the differences in a polynomial of degree 4, 5 and n.
3.
The parabolic reflectors that are used to send and receive microwaves and sounds have
shapes determined by quadratic functions.
Suppose that the profile of one such parabolic dish is given by the graph of
f ( x)  0.05 x 2  1.2 x , where dish width x and depth f(x) are in feet.
a. Sketch a graph of the function f ( x)  0.05 x 2  1.2 x for 0  x  25 . Then write
calculations, equations, and inequalities that would provide answers for parts b - f. Use
algebraic, numeric, or graphic reasoning strategies to find the answers.
b. If the edge of the dish is represented by the points where f(x) = 0, how wide is the dish?
c. What is the depth of the dish at points 6 feet in from the edges?
d. How far in from the edge will the depth of the dish be 2 feet?
e. How far in from the edge will the depth of the dish be at least 3 feet?
f. What is the maximum depth of the dish and at what distance from the edge will that
occur? Label the point (with coordinates) on your graph of f ( x)  0.05 x 2  1.2 x .
4. Imagine you are in charge of constructing a two-tower suspension bridge over the
Potlatch River. You have planned that the curve of the main suspension cables can be
modeled by the function f ( x)  0.004 x 2  x  80 , where f(x) represents height of the
cable above the bridge surface and x represents distance along the bridge surface from
one tower toward the other. The values x and f(x) are measured in feet.
Draw the x-axis (the bridge surface) and the y-axis (the left tower).
a. Sketch a picture.
b. What is the approximate height (from the bridge surface) of each tower from which the
cable is suspended?
c. What is the shortest distance from the cable to the bridge surface and where does it
occur?
d. At which points is the suspension cable at least 50 feet above the bridge surface? Write
an inequality that represents this question and express the solution as an inequality.
5. One formula used by highway safety engineers relates minimum stopping distance f(s) in
feet to vehicle speed s in miles per hour with the rule f ( s)  0.05s 2  1.1s .
a. Create a table of sample (speed, stopping distance) values for a reasonable range of
speeds. Plot the sample (speed, stopping distance) values on a coordinate graph. Then
describe how stopping distance changes as speed increases.
b. Use the stopping distance function to answer the following questions.
i.
What is the approximate stopping distance for a car traveling 60 miles per hour?
ii.
If a car stopped in 120 feet, what is the fastest it could have been traveling when
the driver first noticed the need to stop?
c. Estimate solutions for the following quadratic equations and explain what each solution
tells about stopping distance and speed.
i.
180  0.05s 2  1.1s
ii.
95  0.05s 2  1.1s
6. A professional pyrotechnician shoots fireworks vertically into the air from the ground. It
f (t )  h0  v0t  16t 2
takes 12 seconds for the fireworks to reach the ground.
a. What is the initial velocity? Show work.
b. How long does it take for the fireworks to reach the maximum height? ________
How do you know?
c. What is the maximum height reached by the fireworks?
d. Challenge: Certain fireworks shoot sparks for 2.5 seconds, leaving a trail. After how
many seconds might the pyrotechnician want the fireworks to begin firing in order for
the sparks to be at the maximum height? Explain.
Spiral Review:
7. Consider some familiar measurement formulas.
a. Match the formulas A-D to the measurement calculations they express:
I.
Volume of a cube
A. f ( s)  s 2
II.
Surface area of a cube
B. f ( s)  s 3
III.
Area of a square
C. f ( s)  4s
IV.
Perimeter of a square
D. f ( s)  6s 2
b. Which of the formulas from Part a are those of quadratic functions?
8. Write each of the following exponential expressions in the form 5x for some integer x.
a.
b.
c.
d.
 5  5 
5   5 
5 
4 5   5
3
4
7
3
2 3
3
3
9. Rewrite each expression in a simpler equivalent form by first using the distributive
property and then combining like terms. Write your simplified expression in descending
order (highest power down to constant).
a. 6 x  3x  5  12 x
b. 22  2 15  4x 
c.
1
2
12 x  7    9  15 x 
2
3
d. 15   3x  8  5x  6  3x 