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. August

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 case, V(x) = 2x^2 - 32x + 150 represents 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 how to work with piecewise functions is crucial for correctly applying the appropriate formula based on the month in question.

Function Evaluation

Function evaluation involves substituting a specific input value into a function to find the corresponding output. To find the number of volunteers in August, we need to evaluate V(x) at x = 8 using the quadratic function. This process is fundamental in algebra, as it allows us to derive specific values from general mathematical expressions.