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The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by: m(x)=-(x-5)^(2)+25 What is the maximum possible number of mosquitoes? million mosquitoes

The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:\newlinem(x)=−(x−5)2+25 m(x) = -(x - 5)^{2} + 25 \newlineWhat is the maximum possible number of mosquitoes?\newlinemillion mosquitoes

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Q. The number of mosquitoes in Minneapolis, Minnesota (in millions of mosquitoes) as a function of rainfall (in centimeters) is modeled by:\newlinem(x)=−(x−5)2+25 m(x) = -(x - 5)^{2} + 25 \newlineWhat is the maximum possible number of mosquitoes?\newlinemillion mosquitoes
  1. Parabola Direction: The function m(x)=−(x−5)2+25m(x) = -(x-5)^2 + 25 is a downward opening parabola because the coefficient of the squared term is negative.
  2. Vertex Maximum Value: The vertex of the parabola gives the maximum value since the parabola opens downwards.
  3. Vertex Form: The vertex form of a parabola is m(x)=a(x−h)2+km(x) = a(x-h)^2 + k, where (h,k)(h, k) is the vertex.
  4. Vertex Calculation: For m(x)=−(x−5)2+25m(x) = -(x-5)^2 + 25, the vertex is (5,25)(5, 25).
  5. Vertex Interpretation: The xx-coordinate of the vertex, 55, represents the rainfall in centimeters, and the yy-coordinate, 2525, represents the maximum number of mosquitoes in millions.
  6. Maximum Mosquitoes: So, the maximum possible number of mosquitoes is 2525 million mosquitoes.

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