Question

The number of mosquitoes in brooklyn (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by m(x)=-x(x-4)m(x)=−x(x−4)m, left parenthesis, x, right parenthesis, equals, minus, x, left parenthesis, x, minus, 4, right parenthesis what is the maximum possible number of mosquitoes?

Answer 1

4 Million Mosquitoes is correct.

Explanation:

Answer 2

To find the maximum number of mosquitoes, we are going to find the y-coordinate of vertex of our function, but we are going to expand our function:

`m(x)=-x(x-4)`

`m(x)=-x^2+4x`
Now to find the vertex
`(h,k)` of our quadratic, we are going to use the vertex formula. For a quadratic function of the form
`f(x)=ax^2+bx+c`, its vertex
`(h,k)` is given by the formula
`h= (-b)/(2a)` and
`k=f(h)`.

We can infer from our function that
`a=-1` and
`b=4`, so lets replace those values in our formula:

`h= (-b)/(2a)`

`h= (-4)/(2(-1))`

`h= (-4)/(-2)`

`h=2`

`k=m(h)`

`k=m(2)=-2^2+4(2)`

`k=-4+8`

`k=4`
The vertex
`(h,k)` of our function is
`(2,4)`, so the y-coordinate of the vertex is 4.

Since the y-coordinate of the vertex is the maximum number of mosquitoes, we can conclude that he maximum possible number of mosquitoes is 4.