Solve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by V(x), where V(x)=2x^2-32x+150 between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is mod-eled by V(x)=31x-226. Find the number of volunteers in each of the following months. May

Key Concepts

Quadratic Functions

A quadratic function is a polynomial function of degree two, typically expressed in the form V(x) = ax^2 + bx + c. In this context, V(x) = 2x^2 - 32x + 150 models the number of volunteers from January to August. Understanding how to evaluate quadratic functions is essential for determining the number of volunteers in specific months.

Piecewise Functions

Piecewise functions are defined by different expressions based on the input value. In this problem, V(x) is defined by two different equations: one for January to August and another for August to December. Recognizing when to apply each part of the function is crucial for accurately calculating the number of volunteers for the specified month.

Function Evaluation

Function evaluation involves substituting a specific input value into a function to find the corresponding output. For example, to find the number of volunteers in May (x=5), one must substitute 5 into the appropriate function, V(x) = 2(5)^2 - 32(5) + 150, and calculate the result. Mastery of this concept is necessary for solving the problem effectively.