Answer:
C. 15°F at 3:00 a.m
Step-by-step explanation:
We will start seeing the function they give us, as we can see it is of the form ax ^ 2 + bx + c, this means that it is a parabola.
First we will look the term a of the function
t(h) = 0.5h2 − 5h + 27.5
in this case a = 0.5 , is a positive number so we have a minimum, this point shows us when the temperature reaches its minimum at night.
To obtain it we will have to apply this parabola formula
x = -b / 2a
in this case h = -( -5) / 2(0.5)
h = 5
This 5 represents the hours that have passed since 10:00 p.m.
We add 5 to 10:00 p.m. and get the time that is 3:00 a.m.
Finally we replace the function t with this value, and obtain the value of the minimum temperature
t(h) = 0.5h2 − 5h + 27.5
t(5) = 0.5(5)^2 - 5(5) + 27.5
t = 12.5 - 25 + 27.5
t = 15
C. 15°F at 3:00 a.m
