4. Polynomial Functions

In Exercises 5–6, use the function's equation, and not its graph, to find (a) the minimum or maximum value and where it occurs. (b) the function's domain and its range. $f\left(x\right)=-x^2+14x-106$

Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V\left(x\right)$, where $V\left(x\right)=2x^2-32x+150$ between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, $V\left(x\right)$ is modeled by $V\left(x\right)=31x-226$. Find the number of volunteers in each of the following months. Sketch a graph of $y=V\left(x\right)$ for January through December. In what month are the fewest volunteers available?

Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V\left(x\right)$, where $V\left(x\right)=2x^2-32x+150$ 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 modeled by $V\left(x\right)=31x-226$. Find the number of volunteers in each of the following months.

January

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

October

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

December

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

August

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

May

Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product?

Consider the graph of each quadratic function.

a) Give the domain and range.

Consider the graph of each quadratic function.

(a) Give the domain and range.