Algebra II

Question

The number of mosquitoes M(x), in millions, in a certain area depends on the June rainfall x, in inches, according to the function M(x) = 13x – x². What rainfall produces the maximum number of mosquitoes?
Question 11 options:

1) 6.5 in.

2) 13 in.

3) 0 in.

4) 169 in.

Answer 1

you are given a quadratic equation whose graph is an upside-down parabola, so the maximum of this function occurs at the vertex.  you find the x-coordinate of the vertex from the formula h = -b/(2a); in your case b = 13 & a = -1.  Substitute these numbers carefully into the formula to obtain the x value of vertex, which I call h.

 

Then M(h) gives the y-value of this function, namely the maximum.