Answer:
7 centimeters of rain will produce the maximum number of mosquitoes (49 millions of mosquitoes)
Step-by-step explanation:
we have the function
[tex]m(x)=-x^2+14x[/tex]
where
m(x) is the number of mosquitoes in Anchorage, Alaska (in millions of mosquitoes)
x is the rainfall (in centimeters)
This is a vertical parabola open downward
The vertex represent a maximum
The x-coordinate of the vertex represent the centimeters of rain that will produce the maximum number of mosquitoes
so
Convert the quadratic equation into vertex form
[tex]m(x)=-x^2+14x[/tex]
Factor -1
[tex]m(x)=-(x^2-14x)[/tex]
Complete the square
[tex]m(x)=-(x^2-14x+7^2)+7^2[/tex]
[tex]m(x)=-(x^2-14x+49)+49[/tex]
Rewrite as perfect squares
[tex]m(x)=-(x-7)^2+49[/tex]
The vertex is the point (7,49)
therefore
7 centimeters of rain will produce the maximum number of mosquitoes (49 millions of mosquitoes)
