Modeling With Quadratic Functions Worksheet - Section 2.4 Page 7
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819.
20.
24.
MODELING WITH MATHEMATICS
A baseball is
Human Jump
Frog Jump
thrown up in the air. The table shows the heights
y
y
(3, 1)
y (in feet) of the baseball after x seconds. Write an
4
1.00
(3, 2.25)
equation for the path of the baseball. Find the height
of the baseball after 5 seconds.
0.50
2
( )
5
1,
(4, 0)
9
(0, 0)
0
0.00
Time, x
0
2
4
x
0
2
4
6
0
2
4
x
Distance (feet)
Distance (feet)
Baseball height, y
6
22
22
6
21.
ERROR ANALYSIS
Describe and correct the error in
25.
COMPARING METHODS
You use a system with three
writing an equation of the parabola.
variables to fi nd the equation of a parabola that passes
through the points (−8, 0), (2, −20), and (1, 0). Your
✗
friend uses intercept form to fi nd the equation. Whose
y = a(x − p)(x − q)
y
4
method is easier? Justify your answer.
(3, 4)
4 = a(3 − 1)(3 + 2)
2
26.
MODELING WITH MATHEMATICS
The table shows the
a =
2
—
5
distances y a motorcyclist is from home after x hours.
−2
x
y =
2
(x − 1)(x + 2)
—
(2, 0)
5
Time (hours), x
0
1
2
3
(−1, 0)
Distance (miles), y
0
45
90
135
22.
MATHEMATICAL CONNECTIONS
The area of a
a. Determine what type of function you can use to
rectangle is modeled by the graph where y is the
model the data. Explain your reasoning.
area (in square meters) and x is the width (in meters).
b. Write and evaluate a function to determine the
Write an equation of the parabola. Find the
distance the motorcyclist is from home after
dimensions and corresponding area of one possible
6 hours.
rectangle. What dimensions result in the
maximum area?
27.
USING TOOLS
The table shows the heights
h (in feet) of a sponge t seconds after it was dropped
Rectangles
by a window cleaner on top of a skyscraper.
y
(See Example 4.)
12
8
Time, t
0
1
1.5
2.5
3
(1, 6)
Height, h
280
264
244
180
136
4
(0, 0)
(7, 0)
0
0
4
8
x
a. Use a graphing calculator to create a scatter
Width (meters)
plot. Which better represents the data, a line or a
parabola? Explain.
b. Use the regression feature of your calculator to
23.
MODELING WITH MATHEMATICS
Every rope has a
fi nd the model that best fi ts the data.
safe working load. A rope should not be used to lift a
weight greater than its safe working load. The table
c. Use the model in part (b) to predict when the
shows the safe working loads S (in pounds) for ropes
sponge will hit the ground.
with circumference C (in inches). Write an equation
d. Identify and interpret the domain and range in
for the safe working load for a rope. Find the safe
this situation.
working load for a rope that has a circumference of
(See Example 3.)
10 inches.
28.
MAKING AN ARGUMENT
Your friend states that
quadratic functions with the same x-intercepts have
Circumference, C
0
1
2
3
the same equations, vertex, and axis of symmetry. Is
Safe working
your friend correct? Explain your reasoning.
0
180
720
1620
load, S
Section 2.4
Modeling with Quadratic Functions
81
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