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?

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:


Now to find the vertex  of our quadratic, we are going to use the vertex formula. For a quadratic function of the form , its vertex  is given by the formula  and .

We can infer from our function that  and , so lets replace those values in our formula:








The vertex  of our function is , 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.

I’m not positive but i think it’s none of your buisness