The number of mosquitoes in Brooklyn (in millions of mosquitoes) a function of rainfall (in centimeters) is modeled by \( m(x)=-x(x-4) \) What is the maximum possible number of mosquitoes? million mosquitoes

To find the maximum possible number of mosquitoes modeled by the function \( m(x)=-x(x-4) \), we can rewrite it in vertex form or identify the vertex of the quadratic function. This is a downward-opening parabola, and its maximum occurs at the vertex. The vertex can be found using the formula \( x = -\frac{b}{2a} \), where \( a = -1 \) and \( b = 4 \). Calculating this gives us: \[ x = -\frac{4}{2(-1)} = 2 \] Now, substitute \( x = 2 \) back into the function to find the maximum number of mosquitoes: \[ m(2) = -(2)(2-4) = -2(-2) = 4 \] So, the maximum possible number of mosquitoes is 4 million mosquitoes.