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. October

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.

Piecewise Functions

A piecewise function is defined by different expressions based on the input value. In this scenario, V(x) has two distinct expressions: one for January to August and another for August to December. Recognizing how to apply the correct function based on the month is crucial for accurately calculating the number of volunteers in October.

Function Evaluation

Function evaluation involves substituting a specific input value into a function to find the corresponding output. For October, which corresponds to x=10, we need to use the second piece of the piecewise function, V(x) = 31x - 226. Mastering function evaluation allows us to determine the exact number of volunteers available in that month.