(e) What is the
y
-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth).

5
NONLINEAR MODELS - For the latter part of the quiz, we will explore some nonlinear models.
9. (16
pts)
QUADRATIC REGRESSION
Data:
On a particular summer day, the outdoor temperature was recorded at 8 times of the day, and the following table
was compiled. A scatterplot was produced and the parabola of best fit was determined.
t
=
Time
of day
(hour)
y
= Outdoor
Temperature
(degrees F.)
7
52
9
67
11
73
13
76
14
78
17
79
20
76
23
61
Quadratic Polynomial of Best Fit:
y
=
0.3476
t
2
+ 10.948
t
6.0778
where
t
= Time of day (hour) and
y
= Temperature (in degrees)
REMARKS: The times are the hours since midnight. For instance, 7 means 7 am, and 13 means 1 pm.
(a) Using algebraic techniques we have learned, find the
maximum temperature predicted by the quadratic model
and
find the
time when it occurred.
Report the time to the nearest quarter hour (i.e., __:00 or __:15 or __:30 or __:45). (For
instance, a time of 18.25 hours is reported as 6:15 pm.) Report the maximum temperature to the nearest tenth of a degree.
Show algebraic work.
(b) Use the quadratic polynomial to estimate the outdoor temperature at 7:30 am, to the nearest tenth of a
degree. (work optional)
y = -0.3476t
2
+ 10.948t - 6.0778
R² = 0.9699
0
10
20
30
40
50
60
70
80
90
0
4
8
12
16
Temperature (degrees)
Time of Day (hour)
Temperature
on a Summer Day
20
24

6