Question

The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in

centimeters) is modeled by:
m(x) = -(x - 5)2 + 25
How many centimeters of rainfall will produce the maximum number of mosquitoes?

Answer 1

5 cm

Explanation:

Given the function:

`m(x)=-(x-5)^(2) +25`

As we know the above function is a quadratic equation (vertical parabola) open downward and the vertex is the maximum number of mosquitoes.

The vertex form of a quadratic function is:

`y=a(x-h)^(2) +k` where (h,k) is the vertex

Our given function have the vertex form as well, so the

(h,k) = (5,25)

At the height of 5 cm the rainfall will produce the maximum number of mosquitoes