M110 Modeling with Elementary Functions
V. J. Motto
Fall 2013
Practice Test # 2
Name _________________________________________
Part One: True/False
Place a 0 in front of each false statement and 1 in front of each true statement.
This section is worth 10 points.
_____
1. The point (2.5, 0) is a point of f(x) = (x – 3)(5 – 2x).
_____
2. The point (-5, 0) is the y-intercept for f(x) = – 2x2 – 11x – 5.
_____
3. The graph of f(x) = – 2x2 – 11x – 5 is a linear function.
_____
4. The graph of f(x) = 3x – 5 is a quadratic function.
_____
5. The graph of f(x) = 2x2 – 11x – 5 is a parabola that opens
upward.
_____
6. The graph of f(x) = – 2x2 – 11x – 5 is a parabola that opens
downward.
_____
7. The f(x) = – 2x2 – 11x – 5 has a maximum value at x = 5.5.
_____
8. The function f(x) = – 2x2 – 11x – 5 has a zero at (0, -5 )
_____
9. f(x) = – 2x2 – 11x – 5 and g(x) = 3x intersect in two places.
_____
10. The domain of f(x) = – 2x2 – 11x – 5 is x > -17.
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Part Two:
Analysis.
Show all your work. When possible circle your final answer. This section is
worth 90 points.
Problem # 1
1. Consider the function: f(x) = – 2x2 – 11x – 5
a.
Complete the table of values
x
-3.2
-1.7
-1.3
0
1.4
2.4
3.7
4.2
9.1
b. Sketch the graph of this function labeling the important points.
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f(x)
Problem # 2
A tennis ball is shot into the air from the ground by an air canon upward with a
velocity of 155 ft/sec. Its height s(t) in feet above the grown after t seconds is
given by
s(t) = 144t – 16t2.
a.
b.
c.
d.
e.
What is the height after 3 seconds?
What is the height at 4.3 seconds?
What is the maximum height?
How long is the object in the air?
Draw a graph that represents this situation.
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Problem # 3
The total cost of producing and selling x units of a certain commodity per month
is
C(x) = 1200 + 3.25x – 0.0002x2
a.
b.
c.
d.
e.
Sketch a graph of the function labeling all important points.
What is the maximum cost?
How many units to achieve the maximum cost?
For what values of x is C(x) decreasing?
For what values of x is C(x) increasing?
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Problem # 4
The Olympic flame tower at the 1992 Summer Olympics was lit at a height of 27
m by a flaming arrow that was launched about 63 m from the base of the tower.
If the arrow landed about 63 m beyond the tower, find a quadratic function that
expresses the height h of the arrow as a function of the distance d that it
traveled horizontally.
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Problem # 5
The following table lists prices of pizza at Enzo’s Pizza Place:
Diameter
8 in
12 in
16 in
Price
$6.00
$8.50
$11.50
a. Create both a quadratic and linear model for this data sketching the
graphs.
b. Which model is the best? Why?
c. What is the price of 14-inch pizza?
Linear Model
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Quadratic Model
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Problem # 6
Consider the system of equations:
f(x) = – 2x2 – 11x – 5
g(x) = -x + 3
a. Sketch the graph of this system below labeling the important points.
b. Find the coordinates of the points of intersection (if they exist).
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