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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?

Respuesta :

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

We can infer from our function that [tex]a=-1[/tex] and [tex]b=4[/tex], so lets replace those values in our formula:
[tex]h= \frac{-b}{2a} [/tex]
[tex]h= \frac{-4}{2(-1)} [/tex]
[tex]h= \frac{-4}{-2} [/tex]
[tex]h=2[/tex]
[tex]k=m(h)[/tex]
[tex]k=m(2)=-2^2+4(2)[/tex]
[tex]k=-4+8[/tex]
[tex]k=4[/tex]
The vertex [tex](h,k)[/tex] of our function is [tex](2,4)[/tex], 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:

4 Million Mosquitoes is correct.

Step-by-step explanation:

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