Question 281319
1.) For certain species of insect, a model of the number of larvae, N(T), that survive during this period is given by
N(T)= -0.6T^2 + 32.1T - 350
[T is the temperature in degrees celsius]
a.) At what temperature will the maximum number of larvae survive? Round to the nearest degree. 
Yes, this is a parabola.
Since the coefficient associated with the T^2 term is NEGATIVE, we know that the parabola opens downward.  Thus if we find the "axis of symmetry" it will give us the max temperature.  Axis of symmetry is found by:
x = -b/(2a)
x = -32.1/(2(-0.6))
x = -32.1/(-1.2)
x = 26.75 celsius
.
b.) What is the maximum number of surviving larvae? Round to the nearest whole number
Since N(T) gives us the number as a function of temperature we simply plug in the value found above into:
N(T)= -0.6T^2 + 32.1T - 350
N(26.75)= -0.6(26.75^2) + 32.1(26.75) - 350
N(26.75)= 79
.
c.) find the x-intercepts, to the nearest whole number, for the graph of this function. 
To find the x-intercepts, set N(T) to zero and solve for T:
N(T)= -0.6T^2 + 32.1T - 350
0 = -0.6T^2 + 32.1T - 350
Using the quadratic equation gives you:
T = {15.25, 38.25}
.
d.) Write a sentence that describes the meaning of the x-intercepts in the context of this problem. 
These are the temperatures where no larvae will be produced -- optimum temperatures to rid yourself of this type of insects.