Exam 3: Quadratic and Other Special Functions

The graph of the profit function is given as follows. Consider the average rate of change of the profit from a to 350 where a lies to the left of 350. Does the average rate of change of the profit get closer to 0 or farther from 0 as a gets closer to 350? ​ ​

Find the maximum revenue for the revenue function . Round your answer to the nearest cent.

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. ​

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. ​ ​

Sketch the graph of the function . ​

A fissure in the earth appeared after an earthquake. To measure its vertical depth, a stone was dropped into it, and the sound of the stone's impact was heard 3.3 seconds later. The distance (in feet) the stone fell is given by , and the distance (in feet) the sound traveled is given by . In these equations, the distances traveled by the sound and the stone are the same, but their times are not. Using the fact that the total time is 3.3 seconds, find the depth of the fissure. Round your answer to two decimal places. ​

Determine if the vertex of the graph of the equation is a maximum or minumim point. ​ ​

The table below shows the national expenditures for health care in a certain country for selected years. Find a power model and a linear model for the data where x is the number of years after 1950. Which of the models seems to be the best to use if you are interested in finding the health care costs near the year 1990? Round numerical values in your answers to three decimal places. ​

Determine whether the given graph is the graph of a polynomial function, a rational function (but not a polynomial), or a piecewise defined function. Use the graph to estimate the turning points and any asymptotes. ​ ​

The table shows the average earnings of year-round, full-time workers by gender and educational attainment in a certain country. Let x represent earnings for males and y represent earnings for females, and find a linear model that expresses women's annual earnings as a function of men's. Interpret the slope of the linear model. Round your final values to three decimal places. ​

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

The total costs for a company are given by , and the total revenues are given by . Find the break-even points. ​

Find the x-intercepts, if any exist. Round your answers to two decimal places. ​ ​

Sketch the graph of the function below. ​ ​

Find the exact real solutions of the equation , if they exist. ​

Solve the equation by using the quadratic formula. Give real answers rounded to two decimal places. ​ ​

If a ball is thrown upward at 80 feet per second from the top of a building that is 100 feet high, the height of the ball can be modeled by , where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 100 feet?

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

Solve the equation by using a graphing utility. Round your answers to two decimal places. ​

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