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Polynomial Properties |
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Quadratic, or second-degree, polynomials are of particular interest in many applications. In Lessons 7.6 and 7.7, you graphed quadratic functions. In this activity, you will use an interactive program to graph some cubic, or third-degree, polynomials and observe some of their properties. |
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Internet Activity |
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Activity 7.7
Click this link to view your assignment for this activity.
http://go.hrw.com/resources/go_mt/e1/c7/EZEROS.PDF |
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Adobe Acrobat Reader
You will need Adobe Acrobat Reader to open and print the activity. To download the reader, click "Adobe Acrobat Reader" above.
http://www.adobe.com/products/acrobat/readstep.html |
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Exploration |
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Graphing Cubic Polynomials
This interactive site graphs functions of the form f(x) = ax^3 + bx^2 + cx + d
so you can observe what happens when you change the coefficients a, b, c, and d. At the bottom of the first screen is a brief guide to using the program. If at any time you cannot see your graph on the screen, use the “zoom out” until you can see it, or just click on the “reset” button. Let’s get an idea of what the graph of the simplest cubic function,
f(x) = x^3, looks like. Change the four numbers in the boxes so that a = 1, b = 0, c = 0, and d = 0. Notice what happens at the ends of the graph: the graph drops off the bottom on the left and sails off the top on the right.
http://xanadu.math.utah.edu/java/CubicGraph.html |
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Polynomial Solver
This interactive site estimates the values where the graph of a polynomial crosses the x-axis. Notice that you need to fill in five boxes. The first one is for the coefficient of an x^4 term, which we will not need for this activity. To use the solver, enter 0 in this box, then enter the other coefficients, and click on “Solve.” The solution is displayed inside the box in the middle of your screen.
http://www.homewood.net/java/ |
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