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

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 $h= \frac{-b}{2a}$ and $k=f(h)$.

We can infer from our function that $a=-1$ and $b=4$, so lets replace those values in our formula:
$h= \frac{-b}{2a}$
$h= \frac{-4}{2(-1)}$
$h= \frac{-4}{-2}$
$h=2$
$k=m(h)$
$k=m(2)=-2^2+4(2)$
$k=-4+8$
$k=4$
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.

Answer 2

Answer:

its 2

Step-by-step explanation: