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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?

User WhoIsDT
by
8.2k points

2 Answers

2 votes

Answer:

4 Million Mosquitoes is correct.

Explanation:

User Tavia
by
8.5k points
3 votes
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= (-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= (-b)/(2a)

h= (-4)/(2(-1))

h= (-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.
User TachyonVortex
by
8.2k points
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