The number of mosquitoes $M(x)$, in millions, in a certain area depends on the June rainfall $x$, in inches, according to the formula $M(x)=9 x-x^{2}$. What rainfall produces the maximum number of mosquitoes?
A) 0 in.
B) $81 \mathrm{in.}$
C) 4.5 in.
D) 9 in.

Question

Quizplus · Accepted Answer

The maximum value of $M(x)$ occurs at the vertex of the parabola represented by the quadratic equation. The x-coordinate of the vertex can be found using the formula $-\frac{b}{2a}$ for a quadratic equation in the form $ax^2 + bx + c$. Here, $a = -1$ and $b = 9$, so the x-coordinate of the vertex is $-\frac{9}{2(-1)} = 4.5$. This means the maximum number of mosquitoes occurs when the June rainfall is 4.5 inches.

The Number of Mosquitoes M(x)M(x)M(x) , in Millions, in a Certain Area Depends on the Certain

The Number of Mosquitoes $M(x)$ , in Millions, in a Certain Area Depends on the Certain