Question

The minutes of daylight each day of the year in a certain northern town are approximately modeled by the function

f(x) = -1/25(x-173)^2 + 1424

Where x represents the day of the year (January 1 is x=1) and f(x) represents the minutes of sunlight.

Answer 1

The vertex of this function means that on the longest day of the

year June 22nd (day 173)- this town saw

(Blank) minutes of sunlight.

:1,400

: 1,424

:: 1,350

: 450

:: 175

Answer 2

To find the maximum number of daylight minutes, we need to find the vertex of the parabolic function f(x) = -1/25(x-173)^2 + 1424.

The x-coordinate of the vertex can be found by using the formula x = -b/2a, where a = -1/25 and b = 173.

x = -173 / (2*(-1/25))
x = -173 / (-2/25)
x = -173 * (-25/2)
x = 173 * 25 / 2
x = 4325 / 2
x = 2162.5

Therefore, the maximum number of daylight minutes occurs on day 2162.

To find the maximum number of daylight minutes, plug x = 2162 into the function f(x):
f(2162) = -1/25(2162-173)^2 + 1424
f(2162) = -1/25(1989)^2 + 1424
f(2162) = -1/25 * 3956041 + 1424
f(2162) = -158241.64 + 1424
f(2162) = 141977.36

Therefore, the maximum number of daylight minutes in this town is approximately 141977 minutes.

Answer 3

The correct answer is:

1,424 minutes