The number of mosquitoes in Anchorage,
Alaska (in millions of mosquitoes) as a function
of rainfall (in centimeters) is modeled by:
M(x)=-x^2+12x
After how many inches of rainfall will there not
be any mosquitoes?

After 12 inches of rainfall there not be any mosquitoes

Step-by-step explanation:

The correct question is

The number of mosquitoes in Anchorage,  Alaska (in millions of mosquitoes) as a function  of rainfall (in inches) is modeled by:

M(x)=-x^2+12x

After how many inches of rainfall will there not  be any mosquitoes?

we have

where

M(x) is number of mosquitoes in Anchorage,  Alaska (in millions of mosquitoes)

x is the rainfall in inches

Remember that the x-intercepts are the values of x when the value of the function M(x) is equal to zero

That means ---> The x-intercepts are the values of the rainfall when the number of mosquitoes is equal to zero

Find the x-intercepts

For M(x)=0

Factor -x

The solutions are

x=0 in and x=12 in

therefore

After 12 inches of rainfall there not be any mosquitoes

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .