Creating a Quadratic Model of the Form y = a ( x − h ) 2 + k Estimated time: 20 minutes Group Size: 3 In an earlier group activity, we modeled the path of a softball that was thrown from right field to third base. The data points are given in the table. The values of t represent the time in seconds after the ball was released, and y represents the height of the ball in feet. T i m e ( s e c ) t 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 H e i g h t ( f t ) y 5 11 16 19 21 22 21 19 16 12 6 Use the function found in step 5 to approximate the height of the ball after 0.7 sec.
Creating a Quadratic Model of the Form y = a ( x − h ) 2 + k Estimated time: 20 minutes Group Size: 3 In an earlier group activity, we modeled the path of a softball that was thrown from right field to third base. The data points are given in the table. The values of t represent the time in seconds after the ball was released, and y represents the height of the ball in feet. T i m e ( s e c ) t 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 H e i g h t ( f t ) y 5 11 16 19 21 22 21 19 16 12 6 Use the function found in step 5 to approximate the height of the ball after 0.7 sec.
Solution Summary: The author calculates the height of the ball using the equation y=-17(t-1)2+22.
Creating a Quadratic Model of the Form
y
=
a
(
x
−
h
)
2
+
k
Estimated time: 20 minutes
Group Size: 3
In an earlier group activity, we modeled the path of a softball that was thrown from right field to third base. The data points are given in the table. The values of t represent the time in seconds after the ball was released, and y represents the height of the ball in feet.
T
i
m
e
(
s
e
c
)
t
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
H
e
i
g
h
t
(
f
t
)
y
5
11
16
19
21
22
21
19
16
12
6
Use the function found in step 5 to approximate the height of the ball after 0.7 sec.
Make up two polynomial functions, f(x) and g(x).
• f(x) should be of degree 3 or higher. g(x) should be of degree 4 or higher.
• Find f(3) in each of the three ways: substitution, remainder theorem
(synthetic division), and long division. You should get the same answer
three times for f(3).
Find g(-2) once using your choice of the three methods.
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