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 1.8 sec. How well does this value match the observed value of 12 ft?
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 1.8 sec. How well does this value match the observed value of 12 ft?
Solution Summary: The author calculates the height of the ball using the equation y=-17(t-1)2+22 and compared this value with the observed value 12ft
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 1.8 sec. How well does this value match the observed value of 12 ft?
14
14
4. The graph shows the printing rate of Printer A. Printer B can
print at a rate of 25 pages per minute. How does the printing
rate for Printer B compare to the printing rate for Printer A?
The printing rate for Printer B is
than the rate
for Printer A because the rate of 25 pages per minute
is
than the rate of
for Printer A.
pages per minute
RIJOUT
40
fy
Printer Rat
Number of Pages
8N WA
10
30
20
Printer A
0
0
246
Time (min)
X
OR
16 f(x) =
Ef 16
χ
по
x²-2 410 | y = (x+2) + 4
Y-INT: y = 0
X-INT: X=0
VA: x=2
OA: y=x+2
0
X-INT: X=-2
X-INT: y = 2
VA
0
2
whole.
2-2
4
y - (x+2) = 27-270
+
xxx> 2
क्
above OA
(x+2) OA
x-2/x²+0x+0
2
x-2x
2x+O
2x-4
4
X<-1000 4/4/2<0 below Of
y
VA
X=2
X-2
OA
y=x+2
-2
2
(0,0)
2
χ
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