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The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall X, in inches, according to the equation M(x)=16x-x^2. what rainfall produces the maximum number of mosquitoes? 

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Kenneth S. | Algebra/Trig/Precalculus/Calculus Instructor Can Be Your TutorAlgebra/Trig/Precalculus/Calculus Instru...
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This model is a quadratic equation that opens downwardly because a<0.
Therefore the maximum occurs at the vertex.
The formula for the x coordinate of the vertex is xvertex = -b/(2a) and if you substitute a=-1 and b = 16 you will get a POSITIVE x value.  Then M(x) is the resultant # of mosquitoes.