Now change “d” to “-20” (leaving all other coefficients equal to zero), and create the graph. Change all coefficients to “0” except for “d” (leave it at “20”).
What happens if you change “f” to “0”? Explain.Ĥ. What do you think would happen if you changed “f” to “-30,000”? Try it and explain what happened.ģ. Change the“f” coefficient from “–10,000” to “–20,000.” What is the effect on the roller coaster? Why?Ģ. Use a graphing calculator or spreadsheet program to investigate the effects of the coefficients on the shape of the roller coaster, as follows:ġ. Anybody can plot a function on a computer.
Y =-.015x 6 +.01x 5 + 14x 4 +20x 3 -3000x 2 -10000x + 300000 In this section well focus on how to sketch the graph of any polynomial function, a really important skill. Y = ax 6 +bx 5 + cx 4 +dx 3 +ex 2 + fx + g The shape of a roller coaster could be modeled by a polynomial function, such as this one: Set “a” and “b” equal to zero, and see if you can find values for the other coefficients that produce a graph of this shape: This will cause “humps” to appear in the graph.ħ. Try several other values of “f”, to see the effect. This inverts the graph, causing it to drop from left to right.Ħ. The result is a standard cubic function graph, increasing from left to right.ĥ.
The graph climbs more strongly to the right.Ĥ. What happens if you change “f” to “0”? Explain. What do you think would happen if you changed “f” to “-30,000”? Try it and explain what happened. Eliminate any graphs which don't match this end behavior. As f becomes more negative, that slope increases.Ģ. Step 1: Identify the end behavior of a function's graph using the leading coefficient and degree of the polynomial. “f” is the coefficient of the linear term, and when it has a negative value then that term imparts a negative slope to the graph. Change the “f” coefficient from “–10,000” to “–20,000.” What is the effect on the roller coaster? Why? The roller coaster drops to the right more steeply. You may wish to simplify the activity by restricting the investigation to third or fourth-order polynomials from the beginning.ġ. Students will need to already understand how to enter a polynomial function into a graphing calculator or spreadsheet program. Procedure: This activity is best done by students working individually or in teams of two.
The revenue can be modeled by the polynomial function The revenue in millions of dollars for a fictional cable company from 2006 through 2013 is shown in the table below. Write the equation of a polynomial function given its graph.Draw the graph of a polynomial function using end behavior, turning points, intercepts, and the Intermediate Value Theorem.Identify zeros of polynomial functions with even and odd multiplicity.