Exam 2: Quadratic and Other Special Functions

Suppose that the percent of total personal income that is used to pay personal taxes is given by , where x is the number of years past 1990 (Source: Bureau of Economic Analysis, U.S. Department of Commerce). Find the year or years when the percent of total personal income used to pay personal taxes is 18 percent. ​

Sketch the graph of the function . ​

By recognizing shapes and features of polynomial functions, sketch the graph of the function . Use a graphing utility to confirm your graph. ​

Use a graphing utility to find the vertex of the function. Round your answer to two decimal places. ​ ​

Solve the equation by using the quadratic formula. Give real solutions only. ​ ​

The monthly charge for water in a small town is given by , where x is water usage in hundreds of gallons and f (x) is cost in dollars. Find the monthly charge for 1900 gallons and for 2600 gallons. Round your answers to the nearest cent. ​

Determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. ​ ​

Determine whether the vertex of the graph of the following function is a maximum point or a minimum point. Also find the coordinates of the vertex. ​ ​

Find the vertex of the graph of the equation . ​

If the supply and demand functions for a commodity are given by and , respectively, find the price that will result in market equilibrium. ​

Solve the equation . ​

If a company has total costs , and total revenues given by , find the break-even points. Round your answers to two decimal places. ​

Find the equation of the linear function that is the best fit for the given data. Round your final values to two decimal places. ​

Solve the equation by factoring. ​

A shipping company's charges for delivery of a package is a function of the package's weight. The following table describes the company's shipping rates. ​ ​ Convert this table to a piecewise defined function that represents shipping costs for packages weighing between 0 and 4 pounds using x as the weight in pounds and C as the cost in dollars. Find the postage for a 1.25-pound package. Round your answer to the nearest cent. ​

Determine whether the scatter plot should be modeled by a linear, power, quadratic, cubic, or quartic function. ​ ​

Suppose a company has fixed costs of $26,000 and variable costs of dollars per unit, where x is the total number of units produced. Suppose further that the selling price of its product is dollars per unit. Find the break-even points. Round your answer to the nearest cent. ​

Find the zeros, if any exist. Round your answers to two decimal places. ​ ​

Suppose that the following table gives the number of near-collisions on the runways of the nation's airports. With representing 1990, find a quadratic function that models the data in the chart. Round numerical values in your answer to four decimal places. Depending on the technology you use, your answer may be slightly different than the correct answer shown. ​

In 1995, America's 45 million Social Security recipients received a 2.6% cost-of-living increase, the second smallest increase in nearly 20 years, a reflection of lower inflation. The percent increase might be described by the function , where t is the number of years past 1980. In what year does the model predict the highest cost of living percent increase? ​