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. December

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 models the number of volunteers from January to August. Understanding how to evaluate quadratic functions is essential for determining the number of volunteers during these months.

Linear Functions

A linear function is a polynomial function of degree one, represented as V(x) = mx + b, where m is the slope and b is the y-intercept. For the months from August to December, the number of volunteers is modeled by V(x) = 31x - 226. Recognizing how to work with linear functions is crucial for calculating the number of volunteers in the later months.

Function Evaluation

Function evaluation involves substituting a specific value of x into a function to find the corresponding output. To find the number of volunteers in December, one must evaluate the appropriate function for that month. Since December corresponds to x = 12, understanding how to correctly substitute and compute the value is key to solving the problem.