Determine the quadratic function whose graph is given.
-The number of mosquitoes M(x) , in millions, in a certain area depends on the June rainfall x, in inches: M(x) = 12x - x² . What rainfall produces the maximum number of mosquitoes?

Question

Quizplus · Accepted Answer

The quadratic function is in the form $M(x) = -x^2 + 12x$. The vertex form of a quadratic function is $y = a(x-h)^2 + k$, where $(h, k)$ is the vertex of the parabola. The maximum or minimum value of the quadratic function is at the vertex. For the given function, the vertex can be found using the formula $h = -\frac{b}{2a}$ for a quadratic equation in the form $ax^2 + bx + c$. Here, $a = -1$, $b = 12$, so $h = -\frac{12}{2(-1)} = 6$. This means the maximum number of mosquitoes occurs at 6 inches of rainfall.

Determine the Quadratic Function Whose Graph Is Given