< Quadratic word problems (factored... 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) What amount of rainfall results in the maximum number of mosquitoes? centimeters

To find the amount of rainfall that results in the maximum number of mosquitoes, we need to analyze the quadratic function given by m(x) = -x(x – 4).

The general form of a quadratic function is y = ax^2 + bx + c. The function m(x) = -x(x – 4) can be rewritten in this form as m(x) = -x^2 + 4x.

The maximum or minimum point of a quadratic function is at its vertex. For a quadratic function in the form y = ax^2 + bx + c, the x-coordinate of the vertex is given by -b/(2a). This will give us the amount of rainfall that results in the maximum number of mosquitoes.

Let's apply this to the function m(x).

First, identify a and b from the function m(x) = -x^2 + 4x. Here, a = -1 and b = 4.

Now, apply the formula for the x-coordinate of the vertex: -b/(2a).

x-coordinate of vertex = -b/(2a) = -4/(2 * -1) = -4 / -2 = 2

So, when the rainfall is 2 centimeters, the number of mosquitoes in Brooklyn is at its maximum.